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Mat. Sb., 2009, Volume 200, Number 4, Pages 83–108 (Mi msb6365)  

This article is cited in 19 scientific papers (total in 19 papers)

Blow-up of Oskolkov's system of equations

M. O. Korpusov, A. G. Sveshnikov

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: Oskolkov's system of equations with a cubic source is considered; this describes the dynamics of a viscoelastic fluid. Local solvability (with respect to time) of the problem in the weak generalized sense is proved. Some conditions on the initial function which ensure that the solution blows up in finite time are found, and two-sided estimates for the existence time of the solution are obtained. Moreover, sufficient conditions for the global solvability (with respect to time) of the problem are found.
Bibliography: 19 titles.

Keywords: blow-up for Oskolkov's system of equations, generalized solution, equations of hydrodynamic type.
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English version:
Sbornik: Mathematics, 2009, 200:4, 549–572

Bibliographic databases:

UDC: 517.957
MSC: 76A10, 35Q35, 76D03
Received: 21.05.2008 and 21.11.2008

Citation: M. O. Korpusov, A. G. Sveshnikov, “Blow-up of Oskolkov's system of equations”, Mat. Sb., 200:4 (2009), 83–108; Sb. Math., 200:4 (2009), 549–572

Citation in format AMSBIB
\by M.~O.~Korpusov, A.~G.~Sveshnikov
\paper Blow-up of Oskolkov's system of equations
\jour Mat. Sb.
\yr 2009
\vol 200
\issue 4
\pages 83--108
\jour Sb. Math.
\yr 2009
\vol 200
\issue 4
\pages 549--572

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    This publication is cited in the following articles:
    1. M. O. Korpusov, A. G. Sveshnikov, “Solution blow-up for a new stationary Sobolev-type equation”, Comput. Math. Math. Phys., 50:5 (2010), 831–847  mathnet  crossref  adsnasa  isi  elib
    2. E. V. Yushkov, “Study of the Blow-Up of Solutions of Systems of Equations of Hydrodynamic Type”, Math. Notes, 90:4 (2011), 597–610  mathnet  crossref  crossref  mathscinet  isi
    3. M. O. Korpusov, “On blowup of gravity-gyroscopic waves with nonlinear sources and sinks on the boundary”, Siberian Adv. Math., 22:3 (2012), 161–191  mathnet  crossref  mathscinet
    4. E. V. Yushkov, “On the blow-up of a solution of a non-local system of equations of hydrodynamic type”, Izv. Math., 76:1 (2012), 190–213  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. M. O. Korpusov, “Blow-up of ion-sound waves in plasma with non-linear sources on the boundary”, Izv. Math., 76:2 (2012), 310–345  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. M. O. Korpusov, “Blow-up of the solution of a nonlinear system of equations with positive energy”, Theoret. and Math. Phys., 171:3 (2012), 725–738  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    7. M. O. Korpusov, “On blowup of solutions to a Kirchhoff type dissipative wave equation with a source and positive energy”, Siberian Math. J., 53:4 (2012), 702–717  mathnet  crossref  mathscinet  isi
    8. E. V. Yushkov, “O razrushenii reshenii zadach gidrodinamicheskogo tipa s singulyarnym istochnikom”, Zh. vychisl. matem. i matem. fiz., 52:8 (2012), 1523–1535  mathnet
    9. Korpusov M.O., “On the blow-up of the solution of an equation with a gradient nonlinearity”, Differ. Equ., 48:6 (2012), 796–808  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
    10. E. V. Yushkov, “Blow-Up in Systems with Nonlinear Viscosity”, Math. Notes, 95:4 (2014), 552–564  mathnet  crossref  crossref  mathscinet  isi  elib
    11. E. S. Baranovskii, “Flows of a polymer fluid in domain with impermeable boundaries”, Comput. Math. Math. Phys., 54:10 (2014), 1589–1596  mathnet  crossref  crossref  mathscinet  isi  elib
    12. E. A. Lyzhnik, “Tormozhenie techeniya polimernoi zhidkosti v ploskom kanale”, Mezhdunarodnyi zhurnal prikladnykh i fundamentalnykh issledovanii, 2014, no. 9-3, 168  elib
    13. M. A. Artemov, E. S. Baranovskii, “Granichnye zadachi dlya uravnenii dvizheniya polimernykh zhidkostei c nelineinym usloviem proskalzyvaniya vdol tverdykh stenok”, Tr. IMM UrO RAN, 21, no. 1, 2015, 14–24  mathnet  mathscinet  elib
    14. N. A. Manakova, “Zadacha optimalnogo upravleniya dlya odnoi modeli dinamiki slaboszhimaemoi vyazkouprugoi zhidkosti”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 7:3 (2015), 22–29  mathnet  elib
    15. E. S. Baranovskii, “Mixed initial-boundary value problem for equations of motion of Kelvin–Voigt fluids”, Comput. Math. Math. Phys., 56:7 (2016), 1363–1371  mathnet  crossref  crossref  isi  elib
    16. Baranovskii E.S., “Global Solutions For a Model of Polymeric Flows With Wall Slip”, Math. Meth. Appl. Sci., 40:14 (2017), 5035–5043  crossref  mathscinet  zmath  isi  elib  scopus
    17. M. O. Korpusov, “Solution blow-up in a nonlinear system of equations with positive energy in field theory”, Comput. Math. Math. Phys., 58:3 (2018), 425–436  mathnet  crossref  crossref  isi  elib
    18. Antontsev S.N., de Oliveira H.B., Khompysh Kh., “Generalized Kelvin-Voigt Equations For Nonhomogeneous and Incompressible Fluids”, Commun. Math. Sci., 17:7 (2019), 1915–1948  crossref  mathscinet  zmath  isi
    19. Baranovskii E.S., “Strong Solutions of the Incompressible Navier-Stokes-Voigt Model”, Mathematics, 8:2 (2020), 181  crossref  isi
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