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math.AP2025
Sharp asymptotic stability of the incompressible porous media equation
Roberta Bianchini, Min Jun Jo, Jaemin Park +1
In this paper, we prove the asymptotic stability of the incompressible porous media (IPM) equation near a stable stratified density, for initial perturbations in the Sobolev space…
math.AP2024
Global existence and uniqueness of the density-dependent incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients
Shan Wang
We consider the global well-posedness of the inhomogeneous incompressible Navier-Stokes-Korteweg system with a general capillary term. Based on the maximal regularity property, we…
math.AP2023
Exponential decay results for compressible viscous flows with vacuum
Raphaël Danchin, Shan Wang
We are concerned with the isentropic compressible Navier-Stokes system in the two-dimensional torus, with rough data and vacuum : the initial velocity is in the Sobolev space H^1 a…