Inviscid Limit of the Navier-Stokes-Korteweg Equations under the Weak Kolmogorov Hypothesis in $\mathbb{R}^3$
Year: 2024
Author: Dehua Wang, Cheng Yu
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 3 : pp. 369–383
Abstract
This paper establishes the weak convergence of global solutions for the Navier-Stokes-Korteweg equations under the weak Kolmogorov hypothesis in the three-dimensional periodic domain. Specifically, the weak Kolmogorov hypothesis offers uniform bounds for weak solutions, ensuring their weak stability under vanishing viscosity. With compactness arguments, we show that the solutions of the Navier-Stokes-Korteweg equations converge to a global weak solution of the Euler-Korteweg equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2024-0015
Communications in Mathematical Analysis and Applications, Vol. 3 (2024), Iss. 3 : pp. 369–383
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Inviscid limit Kolmogorov hypothesis Navier-Stokes-Korteweg equations Euler-Korteweg equations compactness.