On the role of pressure in the theory of MHD equations
| Autor: | Minsuk Yang, Jiří Neustupa |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Applied Mathematics Weak solution 010102 general mathematics General Engineering General Medicine Function (mathematics) 01 natural sciences Domain (mathematical analysis) 010101 applied mathematics Section (fiber bundle) Computational Mathematics Distribution (mathematics) No-slip condition Boundary value problem 0101 mathematics Magnetohydrodynamics General Economics Econometrics and Finance Analysis Mathematical physics |
| Zdroj: | Nonlinear Analysis: Real World Applications. 60:103283 |
| ISSN: | 1468-1218 |
| DOI: | 10.1016/j.nonrwa.2020.103283 |
| Popis: | We consider the system of MHD equations in Ω × ( 0 , T ) , where Ω is a domain in R 3 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 Ω 1 × ( t 1 , t 2 ) 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 π ≔ p + 1 2 | b | 2 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 . |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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