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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Uniform tail-ends estimates of the Navier-Stokes equations on unbounded channel-like domains
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by Bixiang Wang
Proc. Amer. Math. Soc. 151 (2023), 4841-4853
DOI: https://doi.org/10.1090/proc/16539
Published electronically: August 22, 2023

Abstract:

This paper deals with the asymptotic compactness of the solutions of the two-dimensional Navier-Stokes equations defined in unbounded channel-like domains. In order to overcome the non-compactness of Sobolev embeddings in unbounded domains, we establish the uniform tail-ends estimates of solutions by showing all the solutions are uniformly small outside a sufficiently large bounded domain for all large time and bounded initial data, which implies the asymptotic compactness and hence the existence of global attractors in the natural energy space. The uniform tail-ends estimates are derived by the scalar stream function of the Navier-Stokes equations which is distinct from the reaction-diffusion equation due to the divergence free condition.
References
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Bibliographic Information
  • Bixiang Wang
  • Affiliation: Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, New Mexico 87801
  • MR Author ID: 314148
  • ORCID: 0000-0001-5851-2453
  • Email: bwang@nmt.edu
  • Received by editor(s): January 17, 2023
  • Received by editor(s) in revised form: April 21, 2023
  • Published electronically: August 22, 2023
  • Communicated by: Wenxian Shen
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4841-4853
  • MSC (2020): Primary 35B40, 35B41, 37L30
  • DOI: https://doi.org/10.1090/proc/16539
  • MathSciNet review: 4634887