2018/02/06 by Jan Březina, Eduard Feireisl, Brezina, Jan +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1802.01785
openalex publication_date 2018/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We identify a large class of objects - dissipative measure-valued (DMV) solutions to the Navier-Stokes-Fourier system - in which the strong solutions are stable. More precisely, a DMV solution coincides with the strong solution emanating from the same initial data as long as the latter exists. The DMV solutions are represented by parameterized families of measures satisfying certain compatibility conditions. They can be seen as an analogue to the dissipative measure-valued solutions introduced earlier in the context of the (inviscid) Euler system.