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arXiv · 2501.18902

Asymptotical Behavior of Global Solutions of the Navier-Stokes-Korteweg Equations with Respect to Capillarity Number at Infinity

Fei Jiang·Pengfei Li·Jiawei Wang
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Abstract

Vanishing capillarity in the Navier-Stokes-Korteweg (NSK) equations has been widely investigated, in particular, it is well-known that the NSK equations converge to the Navier-Stokes (NS) equations by vanishing capillarity number. To our best knowledge, this paper first investigates the behavior of large capillary number, denoted by $\kappa^2$, for the global(-in-time) strong solutions with small initial perturbations of the three-dimensional (3D) NSK equations in a slab domain with Navier(-slip) boundary condition. Under the well-prepared initial data, we can construct a family of global strong solutions of the 3D incompressible NSK equations with respect to $\kappa>0$, where the solutions converge to a unique solution of 2D incompressible NS-like equations as $\kappa$ goes to infinity.

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Fei Jiang, Pengfei Li, Jiawei Wang. 2025-01-31. Asymptotical Behavior of Global Solutions of the Navier-Stokes-Korteweg Equations with Respect to Capillarity Number at Infinity. https://arxiv.org/abs/2501.18902

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