Abstract
Whether or not global solutions of the 2D Navier–Stokes–Cahn–Hilliard (NS–CH) system without full viscosity and mobility can develop finite time singularities is a difficult issue. A major result of this paper deals with global regularity of strong solutions for the NS–CH system with mixed partial viscosity and mobility. In addition, the 2D NS–CH system without viscosity but with full mobility is investigated. In this case, we also prove the global existence and uniqueness of classical solutions.
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