Non-Newtonian fluids with discontinuous-in-time stress tensor

2022/09/21 by Buliček, Miroslav, Gwiazda, Piotr, Skrzeczkowski, Jakub +1 · 1 citation
#35K51 #35Q30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.10695

Abstract

We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically (s-1)-growth with the parameter s depending on the spatial and time variable. We do not assume any smoothness of s with respect to time variable and assume the log-Hölder continuity with respect to spatial variable. Such a setting is a natural choice if the material properties are instantaneously, e.g. by the switched electric field. We establish the long time and the large data existence of weak solution provided that s≥(3d+2)(d+2).

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• Vlasov equation coupled with non-Newtonian fluids with discontinuous-in-time stress tensor

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