Global existence and uniqueness of the density-dependent incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients

2024/08/21 by Wang, Shan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.11675

Abstract

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 obtain the global existence and uniqueness of solutions to the incompressible Navier-Stokes-Korteweg system with variable viscosity and capillary terms. By assuming the initial density ρ₀ is close to a positive constant, additionally, the initial velocity u₀ and the initial density ∇ ρ₀ are small in critical space B^-1+d/p_p,1(\mathbb R^d) (1

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