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Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations (2211.00836v1)

Published 2 Nov 2022 in math.AP

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 $L1$ datum as large-time.

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