Fluids Under Control

0575330 - MÚ 2024 RIV CH eng M - Monography Chapter
Neustupa, Jiří - Yang, M.
On some recent results from the theory of MHD equations.
Fluids Under Control. 1. Cham: Birkhäuser, 2023 - (Bodnár, T.; Galdi, G.; Nečasová, Š.), s. 171-197. Advances in Mathematical Fluid Mechanics. ISBN 978-3-031-27624-8
R&D Projects: GA ČR(CZ) GC22-08633J
Institutional support: RVO:67985840
Keywords : MHD equations * Hall-MHD equations
OECD category: Pure mathematics
https://doi.org/10.1007/978-3-031-27625-5_6

This chapter shows the main ideas of the derivation of the MHD and Hall-MHD equations (Sect. 1) and provides a brief survey of qualitative properties of these equations (Sect. 2). Some results that concern the role of the pressure in the theory of the MHD equations are presented in Sect. 3, and one local regularity criterion for suitable weak solutions to the MHD equations, which uses the behavior of the L3-norm of the velocity and the magnetic field as t approaches the hypothetic singular time t0, is presented in Sect. 4.
Permanent Link: https://hdl.handle.net/11104/0345118