Zeitschrift für Analysis und ihre Anwendungen


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Volume 30, Issue 1, 2011, pp. 83–93
DOI: 10.4171/ZAA/1425

Regularity Criteria in Terms of the Pressure for the Navier-Stokes Equations in the Critical Morrey-Campanato Space

Yong Zhou[1] and Sadek Gala[2]

(1) School of Mathematics, Shanghai University of Finance and Economics, 200433, SHANGHAI, CHINA
(2) Mostaganem University, Department of Mathematics, BP 227, 27000, Mostaganem, ALGERIA

In this paper, we establish a Serrin-type regularity criterion in terms of the pressure for Leray weak solutions to the Navier–Stokes equation in ℝ3. It is proved that the solution is regular if the associate pressure satifies
pL2/2-r ((0, T); M2,3/r (ℝ3)) or ∇pL2/3-r ((0, T); M2,3/r (ℝ3))
for 0 < r < 1, where M2,3/r (ℝ3) is the critical Morrey–Campanto space. Regularity criteria for the 3D MHD equations are also given.

Keywords: Navier–Stokes equations, Morrey–Campanato space, weak solution, regularity criterion

Zhou Yong, Gala Sadek: Regularity Criteria in Terms of the Pressure for the Navier-Stokes Equations in the Critical Morrey-Campanato Space. Z. Anal. Anwend. 30 (2011), 83-93. doi: 10.4171/ZAA/1425