# Partial regularity of solution to generalized Navier-Stokes problem

Open Mathematics (2014)

- Volume: 12, Issue: 10, page 1460-1483
- ISSN: 2391-5455

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topVáclav Mácha. "Partial regularity of solution to generalized Navier-Stokes problem." Open Mathematics 12.10 (2014): 1460-1483. <http://eudml.org/doc/269655>.

@article{VáclavMácha2014,

abstract = {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.},

author = {Václav Mácha},

journal = {Open Mathematics},

keywords = {Stokes problem; Navier-Stokes problem; Partial regularity; Indirect Approach; generalized Navier-Stokes equations; regularity of solutions, singular set},

language = {eng},

number = {10},

pages = {1460-1483},

title = {Partial regularity of solution to generalized Navier-Stokes problem},

url = {http://eudml.org/doc/269655},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Václav Mácha

TI - Partial regularity of solution to generalized Navier-Stokes problem

JO - Open Mathematics

PY - 2014

VL - 12

IS - 10

SP - 1460

EP - 1483

AB - 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.

LA - eng

KW - Stokes problem; Navier-Stokes problem; Partial regularity; Indirect Approach; generalized Navier-Stokes equations; regularity of solutions, singular set

UR - http://eudml.org/doc/269655

ER -

## References

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