Global Existence of Weak Solutions to Chemotaxis Navier-Stokes-Korteweg systems

Abstract: A Chemotaxis compressible Navier–Stokes model was introduced to describe vascular network formation. Global existence for this system was recently shown for adiabatic exponent $\gamma>8/5$ by Huo and J\“ungel. We regularize the equations by adding a Korteweg term and prove global existence for the regularized system, allowing for smaller adiabatic exponents ($\gamma>1$). Our analysis is based on the use of a free energy as well as the BD-entropy, and exploits additional regularity properties derived via the systematic integration-by-parts technique introduced by J\“ungel and Matthes. In the course of this, we can also establish existence results for a broader class of Navier–Stokes–Korteweg systems, which until now have only been investigated in two special cases: the Quantum-Navier–Stokes equation and the thin film equation.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)