Article ID Journal Published Year Pages File Type
5773996 Journal of Differential Equations 2017 49 Pages PDF
Abstract
We investigate the nonlinear thermal instability of the magnetohydrodynamic problem for a full compressible viscous fluid with zero resistivity and zero heat conductivity in the presence of a uniform gravitational force in a bounded domain Ω∈R3. We establish that under some instability conditions, the equilibrium-state is linearly unstable by constructing a suitable energy functional and employing the modified variational method. Then, on the basis of the constructed linearly unstable solutions and the local well-posedness of classical solutions to the original nonlinear problem, we reconstruct the initial data of linearly unstable solutions to be the one of the original nonlinear problem and obtain an appropriate energy estimate of Gronwall-type. Finally, we establish that the equilibrium-state is nonlinearly unstable in view of the energy estimate by a bootstrap method.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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