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Partial regularity of solution to generalized Navier-Stokes problem

100%

Mácha V.

Open Mathematics

2014

tom 12

nr 10

1460-1483

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.

On a generalized Stokes problem

100%

Mácha V.

Open Mathematics

2011

tom 9

nr 4

874-887

We deal with a generalization of the Stokes system. Instead of the Laplace operator, we consider a general elliptic operator and a pressure gradient with small perturbations. We investigate the existence and uniqueness of a solution as well its regularity properties. Two types of regularity are provided. Aside from the classical Hilbert regularity, we also prove the Hölder regularity for coefficients in VMO space.

Ograniczanie wyników

2 Open Mathematics

2 Mácha V.

1 2014

1 2011

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Partial regularity of solution to generalized Navier-Stokes problem

On a generalized Stokes problem