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Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations. (English) Zbl 1198.35175
The authors consider a Log improvement of Prodi-Serrin criterion for global regularity solutions to Navier-Stokes equations in the space, provided the exponents in the Prodi-Serrin criterion are equal to five. The conclusion is that any weak solution to the system satisfying appropriate hypothesis must be smooth for any time and location.
MSC:
35Q30Stokes and Navier-Stokes equations
35B65Smoothness and regularity of solutions of PDE
76D03Existence, uniqueness, and regularity theory
76D05Navier-Stokes equations (fluid dynamics)
35B45A priori estimates for solutions of PDE