On the role of pressure in the theory of MHD equations

0539554 - MÚ 2022 RIV GB eng J - Journal Article
Neustupa, Jiří - Yang, M.
On the role of pressure in the theory of MHD equations.
Nonlinear Analysis: Real World Applications. Roč. 60, August (2021), č. článku 103283. ISSN 1468-1218. E-ISSN 1878-5719
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : MHD equations * pressure * regularity
OECD category: Pure mathematics
Impact factor: 2.765, year: 2021
Method of publishing: Limited access
https://doi.org/10.1016/j.nonrwa.2020.103283

We consider the system of MHD equations in Ω×(0,T), where Ω is a domain in R3 and T>0, with the no slip boundary condition for the velocity u and the Navier-type boundary condition for the magnetic induction b. We show that an associated pressure p, as a distribution with a certain structure, can be always assigned to a weak solution (u,b). The pressure is a function with some rate of integrability if the domain Ω is “smooth”, see section 3. In section 4, we study the regularity of p in a sub-domain Ω1×(t1,t2) of Ω×(0,T), where u (or, alternatively, both u and b) satisfies Serrin's integrability conditions. Regularity criteria for weak solutions to the MHD equations in terms of [Formula presented] are studied in section 5. Finally, section 6 contains remarks on analogous results in the case of Navier's or Navier-type boundary conditions for the velocity u.
Permanent Link: http://hdl.handle.net/11104/0317271