Methods and Applications of Analysis

On a method of holomorphic functions to obtain sharp regularization rates of weak solutions of Navier-Stokes equations

Eugene Tsyganov

Full-text: Open access

Abstract

We show that $L^2$ energy estimates combined with Cauchy integral formula for holomorphic functions can provide bounds for higher-order derivatives of smooth solutions of Navier-Stokes equations. We then extend this principle to weak solutions to improve regularization rates obtained by standard energy methods.

Article information

Source
Methods Appl. Anal., Volume 14, Number 4 (2007), 345-354.

Dates
First available in Project Euclid: 4 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.maa/1225813981

Mathematical Reviews number (MathSciNet)
MR2467105

Zentralblatt MATH identifier
1195.35086

Subjects
Primary: 35B35: Stability
Secondary: 35B40: Asymptotic behavior of solutions 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]

Keywords
Compressible Navier-Stokes equations weak solutions time analyticity holomorphic functions

Citation

Tsyganov, Eugene. On a method of holomorphic functions to obtain sharp regularization rates of weak solutions of Navier-Stokes equations. Methods Appl. Anal. 14 (2007), no. 4, 345--354. https://projecteuclid.org/euclid.maa/1225813981


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