Partial regularity of solution to generalized Navier-Stokes problem

Václav Mácha

Open Mathematics (2014)

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

Abstract

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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.

How to cite

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Václav 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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