квазилинейная симметрическая гиперболическая система, задача со свободной границей,
ударная волна,
сильный разрыв,
устойчивость,
корректность в пространствах Соболева,
магнитная гидродинамика
Гиперболические системы законов сохранения, корректность задач со свободными границами, математическая гидродинамика, ударные волны и характеристические разрывы
Научная биография:
Стажер-исследователь (1993–94), научный сотрудник (1994–96), старший научный сотрудник (1996–2009), ведущий научный сотрудник (2009–2018), главный научный сотрудник (2018 по наст. вр.) Института математики им. С. Л. Соболева СО РАН.
Стипендиат фонда Гумбольдта (1997–98, 2007); стипендиат фонда Карипло/научной сети Ландау (Италия) (2006, 2010, 2012); приглашенный исследователь в университете г. Халл (Англия) (2002–04, 2005); приглашенный DAAD профессор в университете г. Констанц (Германия) (2009); приглашенный профессор в университете г. Брешиа (Италия) (2018); приглашенный профессор в университете г. Констанц (Германия) (2019)
Имею более 70 публикаций.
Основные публикации:
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
Trakhinin Y., “A complete 2D stability analysis of fast MHD shocks in an ideal gas”, Commun. Math. Phys., 236 (2003), 65–92
Trakhinin Y., “Existence of compressible current-vortex sheets: variable coefficients linear analysis”, Arch. Ration. Mech. Anal., 177 (2005), 331–366
Trakhinin Y., “Dissipative symmetrizers of hyperbolic problems and their applications to shock waves and characteristic discontinuities”, SIAM J. Math. Anal., 37 (2006), 1988–2024
Freistühler H., Trakhinin Y., “On the viscous and inviscid stability of magnetohydrodynamic shock waves”, Physica D: Nonlinear Phenomena, 23:1 (2008), 3030–3037
Trakhinin Y., “The existence of current-vortex sheets in ideal compressible magnetohydrodynamics”, Arch. Ration. Mech. Anal., 191 (2009), 245–310
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
Trakhinin Y., “On the well-posedness of a linearized plasma-vacuum interface problem in ideal compressible MHD”, J. Differential Equations, 249 (2010), 2577–2599
Secchi P., Trakhinin Y., “Well-posedness of the plasma-vacuum interface problem”, Nonlinearity, 27 (2014), 105–169
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
Yuri Trakhinin, “Well-posedness of the free boundary problem in compressible elastodynamics”, Journal of Differential Equations, 264 (2018), 1661–1715 , Elsevier BV
Morando A., Trakhinin Y., Trebeschi P., “Local existence of MHD contact discontinuities”, Arch. Ration. Mech. Anal., 228 (2018), 691–742
Morando A., Trakhinin Y., Trebeschi P., “Structural stability of shock waves in 2D compressible elastodynamics”, Mathematische Annalen, 378 (2019), 1471–1504
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
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
Trakhinin Y., Wang T., “Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension”, Mathematische Annalen, 383 (2022), 761–808
Trakhinin Y., Wang T., “Nonlinear Stability of MHD Contact Discontinuities with Surface Tension”, Arch. Ration. Mech. Anal., 243 (2022), 1091–1149
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
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
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.
Ю. Л. Трахинин, “О локальной корректности задач с характеристическими свободными границами для гиперболических систем законов сохранения”, УМН, 79:2(476) (2024), 145–182; 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
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.
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
Yuri Trakhinin, “Well-posedness for moving interfaces in anisotropic plasmas”, Zeitschrift für angewandte Mathematik und Physik, 74 (2023), 142 (12 pp.)
5.
Trakhinin Y., Wang T., “Well-posedness for the free-boundary ideal compressible magnetohydrodynamic equations with surface tension”, Mathematische Annalen, 383 (2022), 761–808
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
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
Ю. Л. Трахинин, “О локальной разрешимости задач со свободными границами в магнитной гидродинамике идеальной сжимаемой жидкости без учета и с учетом поверхностного натяжения”, Прикл. мех. техн. физ., 62:4 (2021), 181–190; 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
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
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
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
Yu. L. Trakhinin, “Local Existence of Contact Discontinuities in Relativistic Magnetohydrodynamics”, Siberian Advances in Mathematics, 30 (2020), 55–76 , Allerton Press ; Yu. L. Trakhinin, “Local existence of contact discontinuities in relativistic magnetohydrodynamics”, Siberian Adv. Math., 30:2 (2020), 55–76
Yuri Trakhinin, “Well-posedness of the free boundary problem in compressible elastodynamics”, Journal of Differential Equations, 264 (2018), 1661–1715 , Elsevier BV
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
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
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
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
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
Yuri Trakhinin, “Existence and Stability of Compressible and Incompressible Current-Vortex Sheets”, Analysis and Simulation of Fluid Dynamics, Birkhäuser Basel, 2006, 229–246
Trakhinin Y., “Dissipative symmetrizers of hyperbolic problems and their applications to shock waves and characteristic discontinuities”, SIAM J. Math. Anal., 37 (2006), 1988–2024
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
Yuri L. Trakhinin, “On Stability of Fast Shock Waves in Classical and Relativistic MHD”, Hyperbolic Problems: Theory, Numerics, Applications, Birkhäuser Basel, 2001, 911–919
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
А. М. Блохин, Ю. Л. Трахинин, И. З. Меражов, “Об устойчивости ударных волн в сплошной среде с объемным зарядом”, Прикл. мех. техн. физ., 39:2 (1998), 29–39; 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
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
А. М. Блохин, Ю. Л. Трахинин, “Симметризация системы уравнений радиационной гидродинамики и глобальная разрешимость задачи Коши”, Сиб. матем. журн., 37:6 (1996), 1256–1265; 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
А. М. Блохин, Ю. Л. Трахинин, “Устойчивость ударных волн для одной модели радиационной гидродинамики”, Прикл. мех. техн. физ., 37:6 (1996), 3–14; 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
А. М. Блохин, Ю. Л. Трахинин, “Исследование устойчивости быстрой магнитогидродинамической ударной волны в плазме с анизотропным давлением”, Прикл. мех. техн. физ., 36:4 (1995), 16–35; 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
41.
A. M. Blokhin, Yu. L. Trakhinin, “Rotational discontinuity in magnetohydrodynamics with anisotropic pressure. I”, Siberian Mathematical Journal, 35 (1994), 9–20 , Springer Science and Business Media LLC ; A. M. Blokhin, Yu. L. Trakhinin, “Rotational discontinuity in magnetohydrodynamics with anisotropic pressure. I”, Siberian Math. J., 35:1 (1994), 9–20
А. М. Блохин, Ю. Л. Трахинин, “Вращательный разрыв в магнитной гидродинамике с анизотропным давлением. II”, Сиб. матем. журн., 35:2 (1994), 278–287; A. M. Blokhin, Yu. L. Trakhinin, “Rotational discontinuity in magnetohydrodynamics with anisotropic pressure. II”, Siberian Math. J., 35:2 (1994), 250–259
А. М. Блохин, Ю. Л. Трахинин, “Об устойчивости ударных волн в магнитной гидродинамике с анизотропным давлением”, Сиб. матем. журн., 34:6 (1993), 10–22; A. M. Blokhin, Yu. L. Trakhinin, “On stability of shock waves in magnetohydrodynamics with anisotropic pressure”, Siberian Math. J., 34:6 (1993), 1005–1016
А. М. Блохин, Ю. Л. Трахинин, “Вращательный разрыв в магнитной гидродинамике”, Сиб. матем. журн., 34:3 (1993), 3–18; A. M. Blokhin, Yu. L. Trakhinin, “Rotational discontinuity in magnetohydrodynamics”, Siberian Math. J., 34:3 (1993), 395–411
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