Manuscript Topics

Generally, the time evolution of the mass density, velocity, and energy density of a compressible viscous fluid is governed by the compressible Navier-Stokes equations (CNS). The incompressible Navier-Stokes equations (whose global well-posedenss and regularity of 3-D large-data solutions is one of Clay's seven millennium problems) may be regarded as the zero Mach number limit of CNS. Owing to the complex mathematical structure, many fundamental questions remain open, including the non-vacuum formation, global existence of solutions with large data, inviscid limit and so on.

The objective of this special issue is the publication of original research on the mathematical analysis of the M-D compressible Navier-Stokes equations and related multiphysyical processes including (but are not limited to): well-posedness theory, singularity formation, non-vacuum formation, inviscid limit, low mach number limit, Radiation hydrodynamics equations, magnetohydrodynamics equations and so on.

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