Navier–Stokes–Fourier System with General Boundary Conditions

2020/09/17 by Eduard Feireisl, Antonín Novotný, Antonin Novotny · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Boundary (topology) #Boundary value problem #Bounded function #Domain (mathematical analysis) #Energy (signal processing) #Flow (mathematics) #Fourier analysis #Fourier series #Fourier transform #Geometry #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Omega #Physics #Stability and Controllability of Differential Equations #Uniqueness #Weak solution #math.AP

paper · pdf · doi:10.1007/s00220-021-04091-1

arxiv created 2020/09/17 · openalex publication_date 2021/04/22 · arxiv updated 2021/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the Navier--Stokes--Fourier system in a bounded domain Ω⊂ R^d, d=2,3, with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative energy inequality. The weak solutions exist globally in time for any finite energy initial data and comply with the weak--strong uniqueness principle.

Citations

• Sur le mouvement d'un liquide visqueux emplissant l'espace
• On the convergence of a finite volume method for the Navier-Stokes-Fourier system
• Dissipative solutions to compressible Navier-Stokes equations with\n general inflow-outflow data: existence, stability and weak strong uniqueness

Cited by

• On Geometric Evolution and Microlocal Regularity of the Navier-Stokes Equations