Author:
Azouz Mohamed,Benabidallah Rachid,Ebobisse François
Abstract
AbstractThis paper is concerned with the study of equations of viscous compressible and heat-conducting full magnetohydrodynamic (MHD) steady flows in a horizontal layer under the gravitational force and a large temperature gradient across the layer. We assume as boundary conditions, periodic conditions in the horizontal directions, while in the vertical directions, slip-boundary is assumed for the velocity, vertical conditions for the magnetic field, and fixed temperature or fixed heat flux are prescribed for the temperature. The existence of stationary solution in a small neighborhood of a stationary profile close to hydrostatic state is obtained in Sobolev spaces as a fixed point of some nonlinear operator.
Publisher
Springer Science and Business Media LLC
Reference47 articles.
1. Alekseev, G.V., Brizitskii, R.V.: Solvability of the mixed boundary value problem for the stationary equations of magnetohydrodynamic equations of a viscous fluid. Dal’nevost. Mat. Zh. 3(2), 285–301 (2002)
2. Alekseev, G.V., Brizitskii, R.V.: Solvability of the boundary value problem for stationary magnetohydrodynamic equations under mixed boundary conditions for the magnetic field. Appl. Math. Lett. 32, 13–18 (2014)
3. Alekseev, G.V., Brizitskii, R.V., Pukhnachev, V.V.: Solvability of the inhomogeneous mixed boundary for stationary magnetohydrodynamic equations. Dokl. Phys. 59, 467–471 (2014)
4. Beirao Da Veiga, H.: Boundary value problems for a class of first order partial differential equations in Sobolev spaces and application to the Euler flow. Rend. Semin. Mat. Univ. Padova 97, 247–273 (1988)
5. Benabidallah, R., Ebobisse, F.: On the stationary solution of a viscous compressible MHD equations. J. Math. Anal. Appl. 519, 126825 (2023)