Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations

Abstract

In this paper, we consider the linearized compressible Navier-Stokes equations in the whole space ${\mathbb{R}}^n$. Concerning initial datum with suitable regularities, we introduce a new threshold $|{\mathbb{B}}_0|=0$ to distinguish different large-time behaviors. Particularly in the lower-dimensions, optimal growth estimates ($n=1$ polynomial growth, $n=2$ logarithmic growth) hold when $|{\mathbb{B}}_0|>0$, whereas optimal decay estimates hold when $|{\mathbb{B}}_0|=0$. Furthermore, we derive asymptotic profiles of solutions with weighted $L^1$ datum as large-time.

References in corpus (1)

• Optimal decay rate of the compressible Navier-Stokes-Poisson system in R^3