The asymptotic profile of solutions to damped Euler equations

Abstract

AbstractThis paper is concerned with the asymptotic behavior of solution to the damped Euler equation far away from vacuum. First of all, the global existence together with the decay rate of the solution and its derivatives are derived by the standard energy method. The decay rates of the solution operator are further improved by Green function method. Finally, the solution of damped Euler equation is confirmed to converge its best asymptotic profile when the initial data is in a certain weighted function space, which establishes the upper and lower bounds of the decay rate to the solution of the damped Euler equation. Here, we provide a new way to check the optimal decay rate of the solutions to the damped Euler equation when the initial data is set in L1, which also could be applied to some other diffusive evolution system.