Well-posedeness And Non-relativistic Limit Analysis For The Free Boundary Value Problem Of The Relativistic Euler Equation

Relativistic hydrodynamics is widely used in astrophysics,plasma physics,nuclear physics and many other fields.However,the relativistic Euler equation is one of the most important mathematical model to study relativistic hydrodynamics.In this thesis,the mathematical results of relativistic Euler equations,especially the results on the free boundary problems,are reviewed.In particular,we will prove the well-posedness and non-relativistic limit of smooth solutions to the one-dimensional relativistic Euler equations.The first chapter is the introduction,which mainly reviews the physical background,the known mathematical results and the main results of this thesis.The second chapter gives the related basic theorems,inequalities and symbols.The third chapter proves the well-posedness and non-relativistic limit of smooth solutions to the free boundary problem of one-dimensional relativistic Euler equation,including the uniform a priori estimate independent of the speed of light c,the degenerate parabolic viscosity approximation,uniqueness and non-relativistic limit.The last chapter states the main difficulties and unsolved problems to study the free boundary problem of the relativistic Euler equation.