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.
Citation
Wenhui Chen. Ryo Ikehata. "Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations." Differential Integral Equations 37 (9/10) 699 - 716, September/October 2024. https://doi.org/10.57262/die037-0910-699
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