Casella, E.; Secchi, P.; Trebeschi, P. Global existence of 2D slightly compressible viscous magneto-fluid motion. (English) Zbl 1001.76117 Port. Math. (N.S.) 59, No. 1, 67-89 (2002). Summary: We study the equations of magneto-hydrodynamics for two-dimensional compressible viscous fluid under periodic boundary conditions. It is well known that, as Mach number goes to zero, the solutions of the compressible model approximate those of the incompressible one. In dimension two such incompressible limit solution is global in time. We prove that also the compressible solution exists for all time, provided that Mach number is sufficiently small, and initial data are almost incompressible. Cited in 3 Documents MSC: 76W05 Magnetohydrodynamics and electrohydrodynamics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q35 PDEs in connection with fluid mechanics 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:global existence; vanishing Mach number; almost incompressible initial data; magneto-hydrodynamics; two-dimensional compressible viscous fluid; periodic boundary conditions; incompressible limit PDFBibTeX XMLCite \textit{E. Casella} et al., Port. Math. (N.S.) 59, No. 1, 67--89 (2002; Zbl 1001.76117) Full Text: EuDML