Partial regularity of solution to generalized Navier-Stokes problem

• Autorzy: Václav Mácha
• Języki publikacji: EN

Abstrakty

EN

In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C 2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension 2 we get even an empty set of singular points.

Słowa kluczowe

EN

Stokes problem; Navier-Stokes problem; Partial regularity; Indirect Approach

Kategorie tematyczne

• 35D30: Weak solutions
• 35B65: Smoothness and regularity of solutions
• 76N10: Existence, uniqueness, and regularity theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 10
• Strony: 1460-1483

Daty

wydano

2014-10-01

online

2014-06-21

Twórcy

autor

Václav Mácha

• Institute of Mathematics AS CR

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-014-0427-9