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May/June 2017 On the local pressure of the Navier-Stokes equations and related systems
Jörg Wolf
Adv. Differential Equations 22(5/6): 305-338 (May/June 2017).

Abstract

In the study of local regularity of weak solutions to systems related to incompressible viscous fluids local energy estimates serve as important ingredients. However, this requires certain information on the pressure. This fact has been used by V. Scheffer in the notion of a suitable weak solution to the Navier-Stokes equations, and in the proof of the partial regularity due to Caffarelli, Kohn and Nirenberg. In general domains, or in case of complex viscous fluid models a global pressure does not necessarily exist. To overcome this problem, in the present paper we construct a local pressure distribution by showing that every distribution $ \partial _t \boldsymbol u +\boldsymbol F $, which vanishes on the set of smooth solenoidal vector fields can be represented by a distribution $ \partial _t \nabla p_h +\nabla p_0 $, where $\nabla p_h \sim \boldsymbol u $ and $ \nabla p_0 \sim \boldsymbol F$.

Citation

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Jörg Wolf. "On the local pressure of the Navier-Stokes equations and related systems." Adv. Differential Equations 22 (5/6) 305 - 338, May/June 2017.

Information

Published: May/June 2017
First available in Project Euclid: 18 March 2017

zbMATH: 06707828
MathSciNet: MR3625590

Subjects:
Primary: 35D05, 35K90, 35Q30, 46E40, 76D05

Rights: Copyright © 2017 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.22 • No. 5/6 • May/June 2017
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