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Trakhinin Yuri Leonidovich
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


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

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