Well-posedness For A Zero Mach Number System In Bounded Domain

This work is devoted to the global well-posedness issue of strong solutions for the 2D zero Mach number system obtained from the full compressible Navier-Stokes equations on bounded domain.The iterative technique and the classical energy method are used to establish the existence and uniqueness of the local strong solution for the zero Mach number system?1.4?.If,in addition,the initial temperature₀is close to the equilibrium statein the sense of^?norm,then we show that the strong solution exists for all positive time.The main content is divided into the following four parts:The introduction mainly introduces the research progress of the zero Mach number system developed from the compressible Navier-Stokes equations,then we briefly derivation model and present our two main research results.The second chapter,we list several facts including some important inequalities and classical lemmas which will be used in the proofs of our main results.The third chapter,the iterative technique and energy estimation method are used to obtain the local existence uniqueness of the strong solution to the zero Mach number system.Combining with the local well-posedness result,we establish the uniform estimate of the local strong solution to obtain the global well-posedness of strong solution,thus we complete the whole proof of theorem.Finally,sum up the main work of this dissertation and propose the direction of future research.