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1998-1999 | 25 | 2 | 221-252
Tytuł artykułu

Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method of successive approximations.
Rocznik
Tom
25
Numer
2
Strony
221-252
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-14
poprawiono
1997-10-17
Twórcy
  • Institute of Mathematics, Śniadeckich 8, 00-950 Warszawa, Poland
  • Institute of Mathematics, Śniadeckich 8, 00-950 Warszawa, Poland
Bibliografia
  • [1] K. O. Friedrichs, Conservation equations and laws of motion in classical physics, Comm. Pure Appl. Math. 31 (1978), 123-131.
  • [2] K. O. Friedrichs, On the laws of relativistic electromagnetofluid dynamics, ibid. 27 (1974), 749-808.
  • [3] K. O. Friedrichs and P. D. Lax, Boundary value problem for the first order operators, ibid. 18 (1965), 355-388.
  • [4] L. Landau and E. Lifschitz, Hydrodynamics, Nauka, Moscow, 1986 (in Russian); English transl.: Fluid Mechanics, Pergamon Press, Oxford, 1987.
  • [5] P. D. Lax and R. S. Phillips, Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math. 13 (1960), 427-455.
  • [6] S. Mizohata, Theory of Partial Differential Equations, Mir, Moscow, 1977 (in Russian).
  • [7] M. Nagumo, Lectures on Modern Theory of Partial Differential Equations, Moscow, 1967 (in Russian).
  • [8] J. Smoller and B. Temple, Global solutions of the relativistic Euler equations, Comm. Math. Phys. 156 (1993), 67-99.
  • [9] W. M. Zajączkowski, Non-characteristic mixed problems for non-linear symmetric hyperbolic systems, Math. Meth. Appl. Sci. 11 (1989), 139-168.
  • [10] W. M. Zajączkowski, Non-characteristic mixed problem for ideal incompressible magnetohydrodynamics, Arch. Mech. 39 (1987), 461-483.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv25i2p221bwm
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