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Mosc. Math. J., 2003, Volume 3, Number 2, Pages 711–737 (Mi mmj107)  

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

Eleven great problems of mathematical hydrodynamics

V. I. Yudovich

Rostov State University

Abstract: The key unsolved problems of mathematical fluid dynamics, their current state and outlook are discussed. These problems concern global existence and uniquness theorems for basic boundary and initial-boundary value problems in the theory of ideal and viscous incompressible fluids, the spectral problems in hydrodynamic stability theory for steady and time periodic flows, creation of secondary, tertiary, etc…flow regimes as a result of bifurcations and the asymptotics of vanishing viscosity. Several new problems are formulated.

Key words and phrases: Incompressible fluid, unsolved problems, existence, uniqueness, stability, asymptotics.


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MSC: 37Nxx, 35Qxx
Received: February 16, 2002

Citation: V. I. Yudovich, “Eleven great problems of mathematical hydrodynamics”, Mosc. Math. J., 3:2 (2003), 711–737

Citation in format AMSBIB
\by V.~I.~Yudovich
\paper Eleven great problems of mathematical hydrodynamics
\jour Mosc. Math.~J.
\yr 2003
\vol 3
\issue 2
\pages 711--737

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    This publication is cited in the following articles:
    1. Yudovich V.I., “Topics in an ideal fluid dynamics”, J. Math. Fluid Mech., 7, suppl. 3 (2005), S299–S325  crossref  mathscinet  zmath  isi
    2. Ohkitani K., “A miscellany of basic issues on incompressible fluid equations”, Nonlinearity, 21:12 (2008), T255–T271  crossref  mathscinet  zmath  isi
    3. Li Y.Ch., Lin Zh., “A Resolution of the Sommerfeld Paradox”, SIAM J Math Anal, 43:4 (2011), 1923–1954  crossref  mathscinet  zmath  isi
    4. Pileckas K., Russo R., “On the existence of vanishing at infinity symmetric solutions to the plane stationary exterior Navier–Stokes problem”, Math Ann, 352:3 (2012), 643–658  crossref  mathscinet  zmath  isi
    5. Li Y.Ch., “Stability Criteria and Turbulence Paradox Problem for Type II 3D Shears”, J. Phys. A-Math. Theor., 45:17 (2012), 175501  crossref  mathscinet  zmath  adsnasa  isi
    6. Korobkov M.V., Pileckas K., Russo R., “On the Flux Problem in the Theory of Steady Navier–Stokes Equations with Nonhomogeneous Boundary Conditions”, Arch. Ration. Mech. Anal., 207:1 (2013), 185–213  crossref  mathscinet  zmath  isi  elib
    7. M. V. Korobkov, K. Pileckas, V. V. Pukhnachov, R. Russo, “The flux problem for the Navier–Stokes equations”, Russian Math. Surveys, 69:6 (2014), 1065–1122  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. Luo G., Hou T.Y., “Potentially Singular Solutions of the 3D Axisymmetric Euler Equations”, Proc. Natl. Acad. Sci. U. S. A., 111:36 (2014), 12968–12973  crossref  isi
    9. Vorobev A., “Dissolution Dynamics of Miscible Liquid/Liquid Interfaces”, Curr. Opin. Colloid Interface Sci., 19:4 (2014), 300–308  crossref  mathscinet  isi  elib
    10. Luo G., Hou T.Y., “Toward the Finite-Time Blowup of the 3D Axisymmetric Euler Equations: a Numerical Investigation”, Multiscale Model. Simul., 12:4 (2014), 1722–1776  crossref  mathscinet  zmath  isi
    11. A. A. Illarionov, L. V. Illarionova, “Statsionarnye resheniya dvumernykh uravnenii Nave–Stoksa s bolshimi potokami”, Dalnevost. matem. zhurn., 15:1 (2015), 61–69  mathnet  elib
    12. Choi K., Kiselev A., Yao Ya., “Finite Time Blow Up For a 1D Model of 2D Boussinesq System”, Commun. Math. Phys., 334:3 (2015), 1667–1679  crossref  mathscinet  zmath  isi
    13. Guillod J., Wittwer P., “Asymptotic Behaviour of Solutions To the Stationary Navier–Stokes Equations in Two-Dimensional Exterior Domains With Zero Velocity At Infinity”, Math. Models Meth. Appl. Sci., 25:2 (2015)  crossref  mathscinet  zmath  isi  elib
    14. A. B. Morgulis, “Variatsionnye printsipy i ustoichivost otkrytykh techenii idealnoi neszhimaemoi zhidkosti”, Sib. elektron. matem. izv., 14 (2017), 218–251  mathnet  crossref
    15. Kiselev A., Yang H., “Analysis of a Singular Boussinesq Model”, Res. Math. Sci., 6 (2018), 13  crossref  mathscinet  isi
    16. Do T., Kiselev A., Xu X., “Stability of Blowup For a 1D Model of Axisymmetric 3D Euler Equation”, J. Nonlinear Sci., 28:6, SI (2018), 2127–2152  crossref  mathscinet  zmath  isi  scopus
    17. Kiselev A., Tan Ch., “Finite Time Blow Up in the Hyperbolic Boussinesq System”, Adv. Math., 325 (2018), 34–55  crossref  mathscinet  zmath  isi  scopus
    18. Luo G., Hou T.Y., “Formation of Finite-Time Singularities in the 3D Axisymmetric Euler Equations: a Numerics Guided Study”, SIAM Rev., 61:4 (2019), 793–835  crossref  mathscinet  zmath  isi  scopus
    19. Alonso-Oran D., de Leon A.B., “Stability, Well-Posedness and Blow-Up Criterion For the Incompressible Slice Model”, Physica D, 392 (2019), 99–118  crossref  mathscinet  isi  scopus
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