Weak solutions to incompressible heat-conducting motions with large flux

2025/06/27 by Joanna Rencławowicz, Rencławowicz, Joanna, Wojciech Zajączkowski +1
Mathematics · Engineering · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.22155

Abstract

We analyze the problem for viscous incompressible heat-conduc\-ting fluid in a finite cylinder with large inflow and outflow, modelled with Navier-Stokes equations coupled with the heat equation. We prove energy estimate without restrictions on the magnitudes of the external force, initial data, inflow and outflow. In order to estimate nonlinear terms we use weighted spaces. Next, using Galerkin approximation, we show existence of weak solutions.

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