Pressure Conditions for the Local Regularity of Solutions of the Navier-Stokes Equations
Date
1998-05-13
Authors
O'Leary, Mike
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We obtain a relationship between the integrability of the pressure gradient and the the integrability of the velocity for local solutions of the Navier--Stokes equations with finite energy. In particular, we show that if the pressure gradient is sufficiently integrable, then the corresponding velocity is locally bounded and smooth in the spatial variables. The result is proven by using De Giorgi type estimates in L(weak)(p) spaces.
Description
Keywords
Navier-Stokes, Regularity, Pressure
Citation
O'Leary, M. (1998). Pressure conditions for the local regularity of solutions of the Navier-Stokes equations. <i>Electronic Journal of Differential Equations, 1998</i>(12), pp. 1-9.
Rights
Attribution 4.0 International