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Low Mach number limit for the global large solutions to the $2$D Navier--Stokes--Korteweg system in the critical $\widehat{L^p}$ framework
In the present paper, we consider the compressible Navier--Stokes--Korteweg system on the $2$D whole plane and show that a unique global solution exists in the scaling critical Fourier--Besov spaces for arbitrary large initial data provided that the Mach number is sufficiently small. Moreover, we also show that the global solution …