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

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.

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    
2. Trakhinin Y., “A complete 2D stability analysis of fast MHD shocks in an ideal gas”, Commun. Math. Phys., 236 (2003), 65–92    
3. Trakhinin Y., “Existence of compressible current-vortex sheets: variable coefficients linear analysis”, Arch. Ration. Mech. Anal., 177 (2005), 331–366    
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    
5. Freistühler H., Trakhinin Y., “On the viscous and inviscid stability of magnetohydrodynamic shock waves”, Physica D: Nonlinear Phenomena, 23:1 (2008), 3030–3037    
6. Trakhinin Y., “The existence of current-vortex sheets in ideal compressible magnetohydrodynamics”, Arch. Ration. Mech. Anal., 191 (2009), 245–310    
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    
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    
9. Secchi P., Trakhinin Y., “Well-posedness of the plasma-vacuum interface problem”, Nonlinearity, 27 (2014), 105–169    
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    
11. Yuri Trakhinin, “Well-posedness of the free boundary problem in compressible elastodynamics”, Journal of Differential Equations, 264 (2018), 1661–1715 , Elsevier BV    
12. Morando A., Trakhinin Y., Trebeschi P., “Local existence of MHD contact discontinuities”, Arch. Ration. Mech. Anal., 228 (2018), 691–742    
13. Morando A., Trakhinin Y., Trebeschi P., “Structural stability of shock waves in 2D compressible elastodynamics”, Mathematische Annalen, 378 (2019), 1471–1504    
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    
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    
16. Trakhinin Y., Wang T., “Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension”, Mathematische Annalen, 383 (2022), 761–808    
17. Trakhinin Y., Wang T., “Nonlinear Stability of MHD Contact Discontinuities with Surface Tension”, Arch. Ration. Mech. Anal., 243 (2022), 1091–1149    
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    
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  
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.  

• Novosibirsk State University
• Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences