Methods and Applications of Analysis

Volume 14 (2007)

Number 4

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

Pages: 345 – 354

DOI: http://dx.doi.org/10.4310/MAA.2007.v14.n4.a3

Author

Eugene Tsyganov

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.

Keywords

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

2010 Mathematics Subject Classification

Primary 35B35. Secondary 35B40, 76N10.

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