Abstract
In this paper, we study the low Mach and Froude number limit of global strong solutions to the fluid‐vacuum free boundary problem of the planar magnetohydrodynamic (MHD) equations with degenerate viscosity coefficients and well‐prepared initial data. Only the initial energy at the basic level is required to be small. The main difficulties are the degeneracy of the system yielded by vanishing of the density close to the free boundary, the singular terms due to the large coefficients inversely proportional to the Mach number and the Froude number, and the strong coupling of the magnetic field and the velocity. The uniform estimates of solutions with respect to the Mach number and the Froude number are established, which is the first result on the MHD equations with vacuum free boundary. At the same time, we obtain the convergence rates for the strong solutions global in time with well‐prepared initial data as the Mach number and the Froude number vanish.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
