| Abstract: | This paper is concerned with the three-dimensional initial boundary-value problem for the equations of magnetohydrodynamics
with additional nonlinear terms stemming from a more general relationship between the electric field and the current density.
The problem governs the motion of a viscous incompressible conducting liquid in a bounded container with an ideal conducting
surface. The existence of a solution which is close to a certain basic solution is proved. The solution is found in the anosotropic
Sobolev spaces W
p
2,1
with p>5/2. The proof relies on the theory of general parabolic initial boundary-value problems. Bibliography: 16 titles.
Dedicated to N. N. Uraltseva on her jubilee
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 167–184.
Translated by V. A. Solonnikov. |
