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arXiv · 2408.11675

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

Shan Wang
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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 $\rho_0$ is close to a positive constant, additionally, the initial velocity $u_0$ and the initial density $\nabla \rho_0$ are small in critical space $\dot B^{-1+d/p}_{p,1}(\mathbb R^{d})$ $(1<p<d).$ This work relies on the maximal regularity property of the heat equation, of the Stokes equation, and of the Lam\'e equation.

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Shan Wang. 2024-08-21. Global existence and uniqueness of the density-dependent incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients. https://arxiv.org/abs/2408.11675

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