# 澳门金沙网址

Local Well-posedness and Incompressible Limit of the free-boundary compressible resistive MHD equations

I will present the proof of local well-posedness and incompressible limit of the free-boundary MHD equations. We apply the tangential smoothing method introduced by Coutand-Shkoller to construct the approximation solutions. One of the key observations is that the Christodoulou-Lindblad elliptic estimates together with magnetic resistivity not only gives the common control of magnetic field and pressure wave, but also controls the Lorentz force as a higher order term in the energy functional. The energy estimates can also be uniform in sound speed and thus the incompressible limit is established.