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arXiv · 1111.4851

On one multidimensional compressible nonlocal model of the dissipative QG equations

Shu Wang·Li Linrui·Shengtao Chen
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Abstract

In this paper we study the Cauchy problem for one multidimensional compressible nonlocal model of the dissipative quasi-geostrophic equations. First, we obtain the local existence and uniqueness of the smooth non-negative solution or the strong solution in time. Secondly, for the sub-critical and critical case $1\le\alpha\leq 2$, we obtain the global existence and uniqueness results of the nonnegative smooth solution. Then, we prove the global existence of the weak solution for $0\le \alpha\le 2$ and $\nu\ge 0$. Finally, for the sub-critical case, we establish the global $H^1$ and $L^p, p>2,$ decay rate of the smooth solution as $t\to\infty$.

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Shu Wang, Li Linrui, Shengtao Chen. 2011-11-21. On one multidimensional compressible nonlocal model of the dissipative QG equations. https://arxiv.org/abs/1111.4851

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