Abstract for the talk at 18.01.2007 (15:00 h)

Kyungkeun Kang (Sungkyunkwan University, Suwon)

On regularity criteria in conjunction with the pressure of the Navier-Stokes equations

We present new regularity criteria involving the integrability of the pressure for the Navier-Stokes equations in bounded domains with smooth boundaries. We prove that either if the pressure belongs to with and or if the gradient of the pressure belongs to with and then weak solutions are regular. Local regularity criteria in terms of pressure are also established near a flat boundary as well as in the interior for suitable weak solutions.