论文标题
关于线性化的可压缩Navier-Stokes方程的大型行为的一些评论
Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations
论文作者
论文摘要
在本文中，我们考虑了整个空间中的线性化可压缩Navier-Stokes方程$ \ Mathbb {r}^n $。关于具有适当规律性的初始基准，我们引入了一个新的阈值$ | \ Mathbb {b} _0 | = 0 $，以区分不同的大型行为。尤其是在较低维度中，当$ | \ m athbb {b} _0 |> 0 $时，最佳增长估计值（$ n = 1 $多项式增长，$ n = 2 $ booggarithmic增长）时，而当$ | \ mathbb {b} _0 _0 _0 | = 0 $ = 0 $ = 0 $。此外，我们得出了具有加权$ l^1 $基准的解决方案的渐近概况。
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.
