| Abstract: |
| In this talk we shall discuss two kinds of singular limits to the isentropic compressible viscous magnetohydrodynamic equations in a bounded domain $\Omega\subset\mathbb{R}^{3}$. One is the incompressible limit, and the other is the inviscid limit. In the first case, the initial data are
assumed to be ``ill-prepared``. We show that the weak solutions (velocity and magnetic field) of the compressible magnetohydrodynamic equations converge weakly in $L^{2}(0,\infty;H^1(\Omega))$ to that of the incompressible viscous magnetohydrodynamic equations. In the other case, the initial data are assumed to be ``well-prepared. It is shown that the weak solutions of the compressible magnetohydrodynamic equations converge strongly in $L^{2}(0,T;L^2(\Omega))$ to the local strong solution of ideal isentropic compressible magnetohydrodynamic equations.
Furthermore, the convergence rates are also obtained. Some related results are also reviewed. |
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