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Volume 3, Issue 3
Inviscid Limit of the Navier-Stokes-Korteweg Equations under the Weak Kolmogorov Hypothesis in $\mathbb{R}^3$

Dehua Wang & Cheng Yu

DOI: 10.4208/cmaa.2024-0015

Commun. Math. Anal. Appl., 3 (2024), pp. 369-383.

Published online: 2024-09

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  • 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.

  • Keywords

Inviscid limit, Kolmogorov hypothesis, Navier-Stokes-Korteweg equations, Euler-Korteweg equations, compactness.

  • AMS Subject Headings

76D05, 35Q31, 35D30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMAA-3-369, author = {Wang , Dehua and Yu , Cheng}, title = {Inviscid Limit of the Navier-Stokes-Korteweg Equations under the Weak Kolmogorov Hypothesis in $\mathbb{R}^3$}, journal = {Communications in Mathematical Analysis and Applications}, year = {2024}, volume = {3}, number = {3}, pages = {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.

}, issn = {2790-1939}, doi = {https://doi.org/10.4208/cmaa.2024-0015}, url = {http://global-sci.org/intro/article_detail/cmaa/23380.html} }
TY - JOUR T1 - Inviscid Limit of the Navier-Stokes-Korteweg Equations under the Weak Kolmogorov Hypothesis in $\mathbb{R}^3$ AU - Wang , Dehua AU - Yu , Cheng JO - Communications in Mathematical Analysis and Applications VL - 3 SP - 369 EP - 383 PY - 2024 DA - 2024/09 SN - 3 DO - http://doi.org/10.4208/cmaa.2024-0015 UR - https://global-sci.org/intro/article_detail/cmaa/23380.html KW - Inviscid limit, Kolmogorov hypothesis, Navier-Stokes-Korteweg equations, Euler-Korteweg equations, compactness. AB -

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.

Wang , Dehua and Yu , Cheng. (2024). Inviscid Limit of the Navier-Stokes-Korteweg Equations under the Weak Kolmogorov Hypothesis in $\mathbb{R}^3$. Communications in Mathematical Analysis and Applications. 3 (3). 369-383. doi:10.4208/cmaa.2024-0015
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