On the low Mach number limit for 2D Navier–Stokes–Korteweg systems

<abstract><p>This paper addresses the low Mach number limit for two-dimensional Navier–Stokes–Korteweg systems. The primary purpose is to investigate relevance of capillarity tensor analysis. For sake a concise exposition, our considerations focus on case quantum Navier-Stokes (QNS) equations. An outline subsequent generalization general viscosity and tensors provided. Our main result proves convergence finite energy weak solutions QNS unique Leray-Hopf incompressible equations, initial data without additional smallness or regularity assumptions. We rely compactness properties stemming from BD-entropy estimates. Strong acoustic waves proven by means refined Strichartz estimates that take into account alteration dispersion relation due tensor. both steps, presence suitable pivotal.</p></abstract>