Time regularity of generalized Navier-Stokes equation with $p(x,t)$-power law

Sin, Cholmin

Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1017-1056

Abstract (VO)

We show time regularity of weak solutions for unsteady motion equations of generalized Newtonian fluids described by $p(x,t)$-power law for $p(x,t)\geq (3n+2)/(n+2)$, $n\geq 2,$ by using a higher integrability property and fractional difference method. Moreover, as its application we prove that every weak solution to the problem becomes a local in time strong solution and that it is unique.

Détail

DOI : 10.21136/CMJ.2023.0033-22

Classification : 35D30, 35D35, 35K92, 76A05
Keywords: weak solution; time regularity; generalized Newtonian fluid, variable exponent

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