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

Volume 25 / 1998

Joanna Rencławowicz, Wojciech Zajączkowski Applicationes Mathematicae 25 (1998), 221-252 DOI: 10.4064/am-25-2-221-252

Abstract

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.

Authors

  • Joanna Rencławowicz
  • Wojciech Zajączkowski

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