Methods and Applications of Analysis
Volume 14 (2007)
On a method of holomorphic functions to obtain sharp regularization rates of weak solutions of Navier-Stokes equations
Pages: 345 – 354
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.
Compressible Navier-Stokes equations; weak solutions; time analyticity; holomorphic functions
2010 Mathematics Subject Classification
Primary 35B35. Secondary 35B40, 76N10.