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

2025/01/31 by Fei Jiang, Pengfei Li, Jiang, Fei +3 · 1 citation
Mathematics · Earth and Planetary Sciences · #Navier-Stokes equation solutions #Aquatic and Environmental Studies

paper · pdf · doi:10.48550/arxiv.2501.18902

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 κ², 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 κ>0, where the solutions converge to a unique solution of 2D incompressible NS-like equations as κ goes to infinity.

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