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 - <p style="text-align: justify;">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.</p>