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On weak-strong uniqueness property for full compressible magnetohydrodynamics flows

100%
Yan W.
Open Mathematics
|
2013
|
tom 11
|
nr 11
2005-2019
EN
This paper is devoted to the study of the weak-strong uniqueness property for full compressible magnetohydrodynamics flows. The governing equations for magnetohydrodynamic flows are expressed by the full Navier-Stokes system for compressible fluids enhanced by forces due to the presence of the magnetic field as well as the gravity and an additional equation which describes the evolution of the magnetic field. Using the relative entropy inequality, we prove that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists.
2
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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
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.
3
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Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains

84%
Borsuk M., Wiśniewski D.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2051-2072
EN
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
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