Author:
Feireisl Eduard,Gwiazda Piotr,Kwon Young-Sam,Świerczewska-Gwiazda Agnieszka
Abstract
AbstractWe propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by ihomogeneous boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime characteristic for turbulence. The weak solutions comply with the weak–strong uniqueness principle; they coincide with the classical solution of the problem as long as the latter exists. The choice of constitutive relations is motivated by applications in stellar magnetoconvection.
Funder
Grantová Agentura Ceské Republiky
Korea National Science Foundation
Narodowe Centrum Badań i Rozwoju
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
Reference27 articles.
1. Alekseev, G.V.: Solvability of control problems for stationary equations of the magnetohydrodynamics of a viscous fluid. Sibirsk. Mat. Zh. 45(2), 243–263 (2004)
2. Alexander, J.C., Auchmuty, G.: $$l^2$$-well-posedness of 3d div-curl boundary value problems. Quart. Appl. Math. 63(3), 479–508 (2005)
3. Battaner, A.: Astrophysical Fluid Dynamics. Cambridge University Press, Cambridge (1996)
4. Buckmaster, T., Cao-Labora, G., Gómez-Serrano, J.: Smooth self-similar imploding profiles to 3d compressible Euler. arxiv preprint No. arXiv:2301.10101 (2023)
5. Chaudhuri, N., Feireisl, E.: Navier–Stokes–Fourier system with Dirichlet boundary conditions. Appl. Anal. 101(12), 4076–4094 (2022)