Analysis of Global Existence and Asymptotic Behavior for the Navier-Stokes Equations

Abstract

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This paper presents an analysis of the global existence and asymptotic behavior of solutions to the two-dimensional compressible Navier-Stokes equations without heat conductivity. The compressible Navier-Stokes equations are a set of partial differential equations used to describe the fluid flow of compressible fluids, such as gases. In this study, the authors consider a simplified version of these equations by removing the heat conductivity term, which simplifies the mathematical model and reduces its computational complexity. The objective of this paper is to establish the global existence of smooth solutions for the simplified version of the compressible Navier-Stokes equations and to investigate their asymptotic behavior. To achieve this goal, the authors employ a combination of energy estimates and perturbation techniques. Specifically, they perform a detailed analysis of the equations and provide proof of the existence and uniqueness of solutions.