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

  • 2020
  • OriginalPaper
  • Chapter
Published in:
Author
Jiří Neustupa
Published in
Fluids Under Pressure
Publisher
Springer International Publishing

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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.

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previous chapter Global Well-Posedness for Incompressible–Incompressible Two-Phase Problem
next chapter Flows of Fluids with Pressure Dependent Material Coefficients
Title
The Role of Pressure in the Theory of Weak Solutions to the Navier-Stokes Equations
Author
Jiří Neustupa
Copyright Year
2020
Book
Fluids Under Pressure

Print ISBN: 978-3-030-39638-1

Electronic ISBN: 978-3-030-39639-8

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-39639-8_4
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