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Trakhinin, Yuri Leonidovich

Total publications: 44 (44)
in MathSciNet: 39 (39)
in zbMATH: 7 (7)
in Web of Science: 6 (6)
in Scopus: 2 (2)
Cited articles: 36
Citations: 595
Presentations: 6

Number of views:
This page:3413
Abstract pages:2039
Full texts:817
References:84
Trakhinin, Yuri Leonidovich
Corresponding member of RAS
Doctor of physico-mathematical sciences (2006)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 24.08.1969
E-mail:
Website: https://a-server.math.nsc.ru/IM/sotrudl.asp?CodID=0000000576
Keywords: quasilinear symmetriс hyperbolic system, free boundary problem, shock wave, strong discontinuity, stability, well-posedness in Sobolev spaces, magnetohydrodynamics
UDC: 517.956.32, 517.956.35, 517.958, 531.327, 551.52, 537.84
MSC: 35L50, 35L65, 35L67, 76L05, 76W05

Subject:

Hyperbolic systems of conservation laws, well-posedness of free boundary problems, mathematical fluid dynamics, shock waves and characteristic discontinuities

Biography

Junior Researcher (1993–94), Researcher (1994–96), Senior Researcher (1996–2009), Leading Researcher (2009–2018), Principal Researcher (2018–now) of the Sobolev Institute of mathematics.
Visiting positions: January 1997 – December 1998, Alexander von Humboldt Research Fellow, University of Stuttgart, Germany; August 2002 – April 2004, Visiting Research Associate, University of Hull, UK; January 2005 – September 2005, Visiting Research Associate, University of Hull, UK; October 2006 – November 2006, Landau Network-Centro Volta-Cariplo Fellow, University of Brescia, Italy; April 2007 – June 2007, Alexander von Humboldt Research Fellow, University of Leipzig, Germany; October 2009 – November 2009, DAAD Visiting Professor, University of Konstanz, Germany; September 2010 – November 2010, Landau Network-Centro Volta-Cariplo Fellow, University of Brescia, Italy; September 2012 – November 2012, Landau Network-Centro Volta-Cariplo Fellow, University of Brescia, Italy, April 2018 – May 2018, Visiting Professor, June 2019, Visiting Professor, University of Konstanz, Germany.

   
Main publications:
  1. Blokhin A., Trakhinin Y., “Stability of strong discontinuities in fluids and MHD”, Handbook of mathematical fluid dynamics, 1, eds. Friedlander S., Serre D., North-Holland, Amsterdam, 2002, 545–652  crossref  mathscinet
  2. Trakhinin Y., “A complete 2D stability analysis of fast MHD shocks in an ideal gas”, Commun. Math. Phys., 236 (2003), 65–92  crossref  mathscinet
  3. Trakhinin Y., “Existence of compressible current-vortex sheets: variable coefficients linear analysis”, Arch. Ration. Mech. Anal., 177 (2005), 331–366  crossref  mathscinet
  4. Trakhinin Y., “Dissipative symmetrizers of hyperbolic problems and their applications to shock waves and characteristic discontinuities”, SIAM J. Math. Anal., 37 (2006), 1988–2024  crossref  mathscinet
  5. Freistühler H., Trakhinin Y., “On the viscous and inviscid stability of magnetohydrodynamic shock waves”, Physica D: Nonlinear Phenomena, 23:1 (2008), 3030–3037  crossref  mathscinet
  6. Trakhinin Y., “The existence of current-vortex sheets in ideal compressible magnetohydrodynamics”, Arch. Ration. Mech. Anal., 191 (2009), 245–310  crossref  mathscinet
  7. Trakhinin Y., “Local existence for the free boundary problem for nonrelativistic and relativistic compressible Euler equations with a vacuum boundary condition”, Comm. Pure Appl. Math., 62 (2009), 1551–1594  crossref  mathscinet
  8. Trakhinin Y., “On the well-posedness of a linearized plasma-vacuum interface problem in ideal compressible MHD”, J. Differential Equations, 249 (2010), 2577–2599  crossref  mathscinet
  9. Secchi P., Trakhinin Y., “Well-posedness of the plasma-vacuum interface problem”, Nonlinearity, 27 (2014), 105–169  crossref  mathscinet
  10. Alessandro Morando, Yuri Trakhinin, Paola Trebeschi, “Well-posedness of the linearized problem for MHD contact discontinuities”, Journal of Differential Equations, 258 (2015), 2531–2571 , Elsevier BV  crossref  mathscinet
  11. Yuri Trakhinin, “Well-posedness of the free boundary problem in compressible elastodynamics”, Journal of Differential Equations, 264 (2018), 1661–1715 , Elsevier BV  crossref  mathscinet
  12. Morando A., Trakhinin Y., Trebeschi P., “Local existence of MHD contact discontinuities”, Arch. Ration. Mech. Anal., 228 (2018), 691–742  crossref  mathscinet
  13. Morando A., Trakhinin Y., Trebeschi P., “Structural stability of shock waves in 2D compressible elastodynamics”, Mathematische Annalen, 378 (2019), 1471–1504  crossref  mathscinet
  14. Lizhi Ruan, Yuri Trakhinin, “Elementary symmetrization of inviscid two-fluid flow equations giving a number of instant results”, Physica D: Nonlinear Phenomena, 391 (2019), 66–71 , Elsevier BV  crossref  mathscinet
  15. Trakhinin Y., Wang T., “Well-posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics”, Arch. Ration. Mech. Anal., 239:2 (2021), 1131–1176  crossref  mathscinet
  16. Trakhinin Y., Wang T., “Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension”, Mathematische Annalen, 383 (2022), 761–808  crossref  mathscinet
  17. Trakhinin Y., Wang T., “Nonlinear Stability of MHD Contact Discontinuities with Surface Tension”, Arch. Ration. Mech. Anal., 243 (2022), 1091–1149  crossref  mathscinet
  18. Trakhinin Y., Wang T., “Well-posedness for moving interfaces with surface tension in ideal compressible MHD”, SIAM J. Math. Anal., 54:6 (2022), 5888–592  crossref  mathscinet
  19. Paolo Secchi, Yuri Trakhinin, Tao Wang, “On vacuum free boundary problems in ideal compressible magnetohydrodynamics”, Bulletin of the London Mathematical Society, 55 (2023), 2087–2111 , Wiley  crossref
  20. Morando A., Secchi P., Trakhinin Y., Trebeschi P., Yuan D., “Well-Posedness of the Two-Dimensional Compressible Plasma-Vacuum Interface Problem”, Archive for Rational Mechanics and Analysis, 248:4 (2024), 56 , 45 pp.  crossref

https://www.mathnet.ru/eng/person17822
https://scholar.google.com/citations?user=u0HCGEkAAAAJ&hl=en
https://zbmath.org/authors/?q=ai:trakhinin.yuri-l
https://mathscinet.ams.org/mathscinet/MRAuthorID/341821
https://elibrary.ru/author_items.asp?authorid=7263
https://orcid.org/0000-0001-8827-2630
https://www.webofscience.com/wos/author/record/D-2229-2009
https://www.scopus.com/authid/detail.url?authorId=55980402200
https://www.researchgate.net/profile/Yuri_Trakhinin

Full list of publications:
| scientific publications | by years | by types | by times cited | common list |


Citations (Crossref Cited-By Service + Math-Net.Ru)

   2024
1. Yu. L. Trakhinin, “On local well-posedness of problems with characteristic free boundary for hyperbolic systems of conservation laws”, Russian Math. Surveys, 79:2 (2024), 325–360  mathnet  crossref  crossref  mathscinet  isi  scopus
2. Morando A., Secchi P., Trakhinin Y., Trebeschi P., Yuan D., “Well-Posedness of the Two-Dimensional Compressible Plasma-Vacuum Interface Problem”, Archive for Rational Mechanics and Analysis, 248:4 (2024), 56 , 45 pp.  crossref

   2023
3. Paolo Secchi, Yuri Trakhinin, Tao Wang, “On vacuum free boundary problems in ideal compressible magnetohydrodynamics”, Bulletin of the London Mathematical Society, 55 (2023), 2087–2111 , Wiley  crossref 4
4. Yuri Trakhinin, “Well-posedness for moving interfaces in anisotropic plasmas”, Zeitschrift für angewandte Mathematik und Physik, 74 (2023), 142 (12 pp.)  crossref  mathscinet

   2022
5. Trakhinin Y., Wang T., “Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension”, Mathematische Annalen, 383 (2022), 761–808  crossref  mathscinet 11
6. Trakhinin Y., Wang T., “Nonlinear Stability of MHD Contact Discontinuities with Surface Tension”, Arch. Ration. Mech. Anal., 243 (2022), 1091–1149  crossref  mathscinet 6
7. Trakhinin Y., Wang T., “Well-posedness for moving interfaces with surface tension in ideal compressible MHD”, SIAM J. Math. Anal., 54:6 (2022), 5888–592  crossref  mathscinet 5

   2021
8. Trakhinin Y., Wang T., “Well-posedness of Free Boundary Problem in Non-relativistic and Relativistic Ideal Compressible Magnetohydrodynamics”, Arch. Ration. Mech. Anal., 239:2 (2021), 1131–1176  crossref  mathscinet 19
9. Yu. L. Trakhinin, “Local solvability of problems with free boundaries in the magnetic hydrodynamics of an ideal compressible fluid with and without account for surface tension”, J. Appl. Mech. Tech. Phys., 62:4 (2021), 684–691  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  elib

   2020
10. Yuri Trakhinin, “On violent instability of a plasma-vacuum interface for an incompressible plasma flow and a nonzero displacement current in vacuum”, Communications in Mathematical Sciences, 18 (2020), 321–337 , International Press of Boston  crossref  mathscinet 6
11. Yuri Trakhinin, “Structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics”, Zeitschrift für angewandte Mathematik und Physik, 71 (2020) , Springer Science and Business Media LLC  crossref  mathscinet 7
12. Alessandro Morando, Paolo Secchi, Yuri Trakhinin, Paola Trebeschi, “Stability of an incompressible plasma–vacuum interface with displacement current in vacuum”, Mathematical Methods in the Applied Sciences, 43 (2020), 7465–7483 , Wiley  crossref  mathscinet 9
13. Yu. L. Trakhinin, “Local existence of contact discontinuities in relativistic magnetohydrodynamics”, Siberian Adv. Math., 30:2 (2020), 55–76  mathnet  crossref  crossref  crossref  mathscinet  scopus

   2019
14. Morando A., Trakhinin Y., Trebeschi P., “Structural stability of shock waves in 2D compressible elastodynamics”, Mathematische Annalen, 378 (2019), 1471–1504  crossref  mathscinet 6
15. Lizhi Ruan, Yuri Trakhinin, “Elementary symmetrization of inviscid two-fluid flow equations giving a number of instant results”, Physica D: Nonlinear Phenomena, 391 (2019), 66–71 , Elsevier BV  crossref  mathscinet 11

   2018
16. Lizhi Ruan, Yuri Trakhinin, “Shock waves and characteristic discontinuities in ideal compressible two-fluid MHD”, Zeitschrift für angewandte Mathematik und Physik, 70 (2018) , Springer Nature  crossref  mathscinet 4
17. Yuri Trakhinin, “Well-posedness of the free boundary problem in compressible elastodynamics”, Journal of Differential Equations, 264 (2018), 1661–1715 , Elsevier BV  crossref  mathscinet 19
18. Morando A., Trakhinin Y., Trebeschi P., “Local existence of MHD contact discontinuities”, Arch. Ration. Mech. Anal., 228 (2018), 691–742  crossref  mathscinet 18

   2015
19. Alessandro Morando, Yuri Trakhinin, Paola Trebeschi, “Well-posedness of the linearized problem for MHD contact discontinuities”, Journal of Differential Equations, 258 (2015), 2531–2571 , Elsevier BV  crossref  mathscinet 14

   2014
20. Secchi P., Trakhinin Y., “Well-posedness of the plasma-vacuum interface problem”, Nonlinearity, 27 (2014), 105–169  crossref  mathscinet 58

   2013
21. Paolo Secchi, Yuri Trakhinin, “Well-posedness of the linearized plasma-vacuum interface problem”, Interfaces and Free Boundaries, 15 (2013), 323–357 , European Mathematical Society - EMS - Publishing House GmbH  crossref  mathscinet 31

   2012
22. Yu Trakhinin, “Stability of Relativistic Plasma–Vacuum Interfaces”, Journal of Hyperbolic Differential Equations, 09 (2012), 469–509 , World Scientific Pub Co Pte Ltd.  crossref  mathscinet 20
23. Yuri Trakhinin, “Well-posedness of the Free Boundary Problem for Non-relativistic and Relativistic Compressible Euler Equations with a Vacuum Boundary Condition”, Series in Contemporary Applied Mathematics, Co-Published with Higher Education Press, 2012, 692–699  crossref  mathscinet

   2010
24. Trakhinin Y., “On the well-posedness of a linearized plasma-vacuum interface problem in ideal compressible MHD”, J. Differential Equations, 249 (2010), 2577–2599  crossref  mathscinet 35

   2009
25. Trakhinin Y., “The existence of current-vortex sheets in ideal compressible magnetohydrodynamics”, Arch. Ration. Mech. Anal., 191 (2009), 245–310  crossref  mathscinet 85
26. Trakhinin Y., “Local existence for the free boundary problem for nonrelativistic and relativistic compressible Euler equations with a vacuum boundary condition”, Comm. Pure Appl. Math., 62 (2009), 1551–1594  crossref  mathscinet 61

   2008
27. Y. Trakhinin, “On Compressible Current–Vortex Sheets”, Hyperbolic Problems: Theory, Numerics, Applications, Springer Berlin Heidelberg, 2008, 209–220  crossref  mathscinet  zmath
28. Freistühler H., Trakhinin Y., “On the viscous and inviscid stability of magnetohydrodynamic shock waves”, Physica D: Nonlinear Phenomena, 23:1 (2008), 3030–3037  crossref  mathscinet 12

   2006
29. Yuri Trakhinin, “Existence and Stability of Compressible and Incompressible Current-Vortex Sheets”, Analysis and Simulation of Fluid Dynamics, Birkhäuser Basel, 2006, 229–246  crossref  mathscinet 1
30. Trakhinin Y., “Dissipative symmetrizers of hyperbolic problems and their applications to shock waves and characteristic discontinuities”, SIAM J. Math. Anal., 37 (2006), 1988–2024  crossref  mathscinet 8

   2005
31. Trakhinin Y., “Existence of compressible current-vortex sheets: variable coefficients linear analysis”, Arch. Ration. Mech. Anal., 177 (2005), 331–366  crossref  mathscinet 56

   2003
32. Trakhinin Y., “A complete 2D stability analysis of fast MHD shocks in an ideal gas”, Commun. Math. Phys., 236 (2003), 65–92  crossref  mathscinet 20

   2002
33. Blokhin A., Trakhinin Y., “Stability of strong discontinuities in fluids and MHD”, Handbook of mathematical fluid dynamics, 1, eds. Friedlander S., Serre D., North-Holland, Amsterdam, 2002, 545–652  crossref  mathscinet 40

   2001
34. Yuri L. Trakhinin, “On Stability of Fast Shock Waves in Classical and Relativistic MHD”, Hyperbolic Problems: Theory, Numerics, Applications, Birkhäuser Basel, 2001, 911–919  crossref  mathscinet

   1999
35. A.M. Blokhin, Yu.L. Trakhinin, “Stability of fast parallel MHD shock waves in polytropic gas”, European Journal of Mechanics - B/Fluids, 18 (1999), 197–211 , Elsevier BV  crossref  mathscinet  adsnasa 9

   1998
36. A. M. Blokhin, Yu. L. Trakhinin, I. Z. Merazhov, “On the stability of shock waves in a continuous medium with a space charge”, J. Appl. Mech. Tech. Phys., 39:2 (1998), 184–193  mathnet  crossref

   1996
37. A. M. Blokhin, Yu. L. Trakhinin, “Shock-wave stability for one model of radiation hydrodynamics”, Journal of Applied Mechanics and Technical Physics, 37 (1996), 775–784 , Springer Science and Business Media LLC  crossref  mathscinet  adsnasa 1
38. A. M. Blokhin, Yu. L. Trakhinin, “Symmetrization of a system of equations of radiative hydrodynamics, and global solvability of the Cauchy problem”, Siberian Math. J., 37:6 (1996), 1101–1109  mathnet  crossref  mathscinet  zmath  isi
39. A. M. Blokhin, Yu. L. Trakhinin, “Shock-wave stability for one model of radiation hydrodynamics”, J. Appl. Mech. Tech. Phys., 37:6 (1996), 775–784  mathnet  crossref

   1995
40. A. M. Blokhin, Yu. L. Trakhinin, “Stability of a fast magnetohydrodynamic shock wave in plasma with anisotropic pressure”, J. Appl. Mech. Tech. Phys., 36:4 (1995), 496–512  mathnet  crossref

   1994
41. A. M. Blokhin, Yu. L. Trakhinin, “Rotational discontinuity in magnetohydrodynamics with anisotropic pressure. I”, Siberian Math. J., 35:1 (1994), 9–20  mathnet  crossref  crossref  mathscinet  zmath  isi
42. A. M. Blokhin, Yu. L. Trakhinin, “Rotational discontinuity in magnetohydrodynamics with anisotropic pressure. II”, Siberian Math. J., 35:2 (1994), 250–259  mathnet  crossref  mathscinet  zmath  isi

   1993
43. A. M. Blokhin, Yu. L. Trakhinin, “On stability of shock waves in magnetohydrodynamics with anisotropic pressure”, Siberian Math. J., 34:6 (1993), 1005–1016  mathnet  crossref  mathscinet  zmath  isi
44. A. M. Blokhin, Yu. L. Trakhinin, “Rotational discontinuity in magnetohydrodynamics”, Siberian Math. J., 34:3 (1993), 395–411  mathnet  crossref  mathscinet  zmath  isi

Presentations in Math-Net.Ru
1. О локальной разрешимости задач со свободными границами для гиперболических систем законов сохранения
Yu. L. Trakhinin
Mathematical Colloquium of the Sobolev Institute of Mathematics
October 6, 2022 16:30
2. On local solvability of a problem with free boundary plazma-vacuum in the magnetohydrodynamics of perfect compressible fluid
Yu. L. Trakhinin
V. I. Smirnov Seminar on Mathematical Physics
September 27, 2021 13:30   
3. Локальная разрешимость задачи со свободной границей для магнитогидродинамического контактного разрыва
Yu. L. Trakhinin

August 13, 2021 09:30
4. On local existence and violent instabilities of a plasma-vacuum interface
Yu. L. Trakhinin
Dynamics in Siberia - 2019
February 25, 2019 12:00
5. О локальной разрешимости в пространствах Соболева задачи со свободной границей для магнитогидродинамического контактного разрыва
Yu. L. Trakhinin
VIII Internet video conference "Day of Mathematics and Mechanics"
September 17, 2018
6. On application of the Nash–Moser method to weakly well-posed free boundary problems
Yu. L. Trakhinin
Dynamics in Siberia - 2018
March 1, 2018 11:30

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