具有对数超耗散的非齐次Navier-Stokes方程的全局适定性和指数衰减

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2023-02-02 DOI:10.1090/qam/1644

Dehua Wang, Z. Ye

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引用次数: 0

摘要

研究了高维非齐次不可压缩对数超耗散Navier-Stokes方程的Cauchy问题。利用Littlewood-Paley技术和新思想，建立了在整个空间R n \mathbb {R}^{n}上具有真空的全局强解的存在唯一性。此外，我们还得到了强解的指数时间衰减。我们的结果在初始数据上没有任何小，并且允许初始密度有真空。

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Global well-posedness and exponential decay for the inhomogeneous Navier-Stokes equations with logarithmical hyper-dissipation

We consider the Cauchy problem for the inhomogeneous incompressible logarithmical hyper-dissipative Navier-Stokes equations in higher dimensions. By means of the Littlewood-Paley techniques and new ideas, we establish the existence and uniqueness of the global strong solution with vacuum over the whole space R n \mathbb {R}^{n} . Moreover, we also obtain the exponential decay-in-time of the strong solution. Our result holds without any smallness on the initial data and the initial density is allowed to have vacuum.

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.