Special Session 2: New frontiers in the compressible mathematical fluid mechanics and thermodynamics

Weak-Strong Uniqueness and Relaxation Limit for a Navier-Stokes-Korteweg Model
Nilasis Chaudhuri
University of Warsaw
Poland
Co-Author(s):    Christian Rohde, Florian Wendt
Abstract:
In this talk, we explore a relaxation model for a compressible fluid with capillarity effects in an isothermal setting. The model involves two parameters that control the strength of the relaxation and are expected to drive the system toward the classical compressible Navier--Stokes--Korteweg equations in an appropriate limiting regime. We introduce a notion of finite-energy weak solutions for the associated initial--boundary value problem in three spatial dimensions. Within this framework, we establish a weak--strong uniqueness result. In addition, we provide a first rigorous justification of the relaxation model by proving convergence to the target system in the relaxation limit at the level of finite-energy weak solutions.