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Uniqueness and regularity of flows of non-Newtonian fluids with critical power-law growth

Banff International Research Station for Mathematical Innovation and Discovery

We deal with the flows of non-Newtonian fluids in three dimensional setting subjected to the homogeneous Dirichlet boundary condition. Under the natural monotonicity, coercivity and growth condition on the Cauchy stress tensor expressed by a critical power index $p=\frac{11}{5}$ we show that a Gehring type argument is applicable which allows to improve regularity of any weak solution. Improving further the regularity of weak solutions along a regularity ladder allows to show that actually solution belongs to a uniqueness class provided data of the problem are sufficiently smooth. </p>

We also briefly discuss if the similar technique is applicable to critical Convective Brinkman-Forchheimer equation.</p>

Mathematics; Partial differential equations; Fluid mechanics; Fluid dynamics

video/mp4

Author affiliation: Charles University

2021-05-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/78437

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/