Study On The Pressure Differential Equation, Initial Boundary Value Problem

The pressure-gradient equations are approximate models of Euler equations, either in theory or in practice it is very important to study it.There are two goals in this paper, one is to compare the solutions of the Euler equation and pressure-gradient equation with the same initial and boundary values, the other is to study the axial symmetric solution of pressure-gradient equation with initial-boundary values.This paper is organized as follows:Chapter one is an introduction. It is devoted to introducing the physical back-ground and the main result and methods.In Chapter two, we do some estimate on the degree of approximation between the solution of Euler equation and pressure-gradient equation. We can prove that the differences between their solutions of the initial-boundary value problems are bounded by O(1)tεIn Chapter three, we prove the local existence of solution of two dimensional axial symmetric pressure-gradient equations with initial and boundary values,by construct-ing Glimm functional and doing some interaction estimates, we have proved the exis-tence of bounded variation solution when 1< t< T,for a suitable constant T> 1...