Fluids Under Pressure

0524152 - MÚ 2021 RIV CH eng M - Monography Chapter
Neustupa, Jiří
The role of pressure in the theory of weak solutions to the Navier-Stokes equations.
Fluids Under Pressure. 1. Basel: Springer, 2020 - (Bodnár, T.; Galdi, G.; Nečasová, Š.), s. 349-416. Advances in Mathematical Fluid Mechanics. ISBN 978-3-030-39638-1
R&D Projects: GA ČR GA16-03230S
Institutional support: RVO:67985840
Keywords : viscous incompressible fluid * Navier-Stokes equations * weak solutions * associated pressure
OECD category: Pure mathematics
https://doi.org/10.1007/978-3-030-39639-8_4

Sections 1 and 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 section 3. The interior regularity of the pressure in regions, where the velocity satisfies Serrin's integrability conditions, is studied in section 4. Finally, section 5 is devoted to criteria of regularity for weak solutions to the Navier-Stokes equations, formulated in terms of the pressure.
Permanent Link: http://hdl.handle.net/11104/0308516