On the stability of compressible Navier–Stokes–Korteweg equations
Volume 111 / 2014
Annales Polonici Mathematici 111 (2014), 149-163
MSC: Primary 35Q35.
DOI: 10.4064/ap111-2-4
Abstract
We consider the compressible Navier–Stokes–Korteweg (N-S-K) equations. Through a remarkable identity, we reveal a relationship between the quantum hydrodynamic system and capillary fluids. Using some interesting inequalities from quantum fluids theory, we prove the stability of weak solutions for the N-S-K equations in the periodic domain $\varOmega =\mathbb {T}^{N}$, when $N=2,3$.
