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The Role of Pressure in the Theory of Weak Solutions to the Navier-Stokes Equations

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Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Abstract

Sections 4.1 and 4.2 contain an introduction, notation and definitions and basic properties of used function spaces and operators. A pressure, associated with a weak solution to the Navier-Stokes equations for incompressible fluid, is constructed in Sect. 4.3. The interior regularity of the pressure in regions, where the velocity satisfies Serrin’s integrability conditions, is studied in Sect. 4.4. Finally, Sect. 4.5 is devoted to criteria of regularity for weak solutions to the Navier-Stokes equations, formulated in terms of the pressure.

Keywords

Viscous incompressible fluid Navier-Stokes equations Weak solutions Associated pressure Regularity 

MSC2010:

35Q30 35Q35 76D03 76D05 

Notes

Acknowledgements

The author has been supported by the Mathematical Institute of the Czech Academy of Sciences (RVO 67985840) and by the Czech Science Foundation (grant No. 16-03230S).

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  1. 1.Institute of Mathematics CASPragueCzech Republic

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