Existence and stability of steady-state solutions to the quasi-geostrophic equations in ℝ2
Existence and stability of steady-state solutions to the quasi-geostrophic equations in ℝ2
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DOI：
10.1088/0951-7715/28/11/4227
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发表时间：
2015-03
期刊：
影响因子：
1.7
通讯作者：
Mimi Dai
中科院分区：
文献类型：
--
作者：
Mimi Dai
我们考虑整个空间R2 ？在f的某些小假设下，我们建立了具有有限L2范数的解的存在性。这个解在所有能量有限的解中是唯一的。唯一的解决方案Θ ？>在以下意义上也被证明是稳定的：由f驱动并以有限能量开始的演化准地转方程的任何解将返回到Θ ？>。
We consider the stationary quasi-geostrophic equation in the whole space R2 ?> driven by a force f. Under certain smallness assumptions of f, we establish the existence of solutions with finite L2 norm. This solution is unique among all solutions with finite energy. The unique solution Θ ?> is also shown to be stable in the sense: any solution of the evolutionary quasi-geostrophic equation driven by f and starting with finite energy, will return to Θ ?>.