On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions

Miroslav Bulíček; Roger Lewandowski; Josef Málek

Displaying similar documents to “On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions”

Planar flows of incompressible heat-conducting shear-thinning fluids — existence analysis

Miroslav Bulíček, Oldřich Ulrych (2011)

Applications of Mathematics

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We study the flow of an incompressible homogeneous fluid whose material coefficients depend on the temperature and the shear-rate. For large class of models we establish the existence of a suitable weak solution for two-dimensional flows of fluid in a bounded domain. The proof relies on the reconstruction of the globally integrable pressure, available due to considered Navier’s slip boundary conditions, and on the so-called $L^{\infty}$ -truncation method, used to obtain the strong convergence of...

On the uniqueness of weak solutions for the 3D Navier-Stokes equations

Qionglei Chen, Changxing Miao, Zhifei Zhang (2009)

Annales de l'I.H.P. Analyse non linéaire

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On the Navier-Stokes equations with temperature-dependent transport coefficients.

Feireisl, Eduard, Málek, Josef (2006)

Differential Equations & Nonlinear Mechanics

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On the blow up criterion for the 2-D compressible Navier-Stokes equations

Lingyu Jiang, Yidong Wang (2010)

Czechoslovak Mathematical Journal

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Motivated by [10], we prove that the upper bound of the density function $ρ$ controls the finite time blow up of the classical solutions to the 2-D compressible isentropic Navier-Stokes equations. This result generalizes the corresponding result in [3] concerning the regularities to the weak solutions of the 2-D compressible Navier-Stokes equations in the periodic domain.

The role of oscillations in the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations

Jean-Yves Chemin, Ping Zhang (2005-2006)

Séminaire Équations aux dérivées partielles

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Corresponding to the wellposedness result [] for the classical 3-D Navier-Stokes equations $(N S_{ν})$ with initial data in the scaling invariant Besov space, $ℬ_{p, \infty}^{- 1 + \frac{3}{p}},$ here we consider a similar problem for the 3-D anisotropic Navier-Stokes equations $(A N S_{ν}),$ where the vertical viscosity is zero. In order to do so, we first introduce the Besov-Sobolev type spaces, $ℬ_{4}^{- \frac{1}{2}, \frac{1}{2}}$ and $ℬ_{4}^{- \frac{1}{2}, \frac{1}{2}} (T) .$ Then with initial data in the scaling invariant space $ℬ_{4}^{- \frac{1}{2}, \frac{1}{2}},$ we prove the global wellposedness for $(A N S_{ν})$ provided the norm of initial data is small...