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Online ISSN 1552-4485; Print ISSN 0033-569X
Global well-posedness and exponential decay for the inhomogeneous Navier-Stokes equations with logarithmical hyper-dissipation
Authors:
Dehua Wang and Zhuan Ye
Journal:
Quart. Appl. Math. 81 (2023), 307-327
MSC (2020):
Primary 35Q35, 35B65, 76N10, 76D05
DOI:
https://doi.org/10.1090/qam/1644
Published electronically:
February 2, 2023
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: 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 $\mathbb {R}^{n}$. 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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Additional Information
Dehua Wang
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260
MR Author ID:
609444
Email:
dwang@math.pitt.edu
Zhuan Ye
Affiliation:
Department of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China
Email:
yezhuan815@126.com
Keywords:
Navier-Stokes equations,
vacuum,
inhomogeneous,
incompressible,
logarithmical hyper-dissipation,
exponential decay,
global strong solution
Received by editor(s):
September 20, 2022
Published electronically:
February 2, 2023
Additional Notes:
The work of the first author was partially supported by the National Science Foundation under grants DMS-1907519 and DMS-2219384. This work of the second author was supported by the Qing Lan Project of Jiangsu Province. The second author is the corresponding author.
Dedicated:
Dedicated to Professor Constantine Dafermos on the occasion of his 80th birthday
Article copyright:
© Copyright 2023
Brown University