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

Miroslav Bulíček; Roger Lewandowski; Josef Málek

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 1, page 89-114
  • ISSN: 0010-2628

Abstract

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In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity ν polynomially increasing with a scalar quantity k that evolves according to an evolutionary convection diffusion equation with the right hand side ν ( k ) | 𝖣 ( v → ) | 2 that is merely L 1 -integrable over space and time. We also formulate a conjecture concerning regularity of such a solution.

How to cite

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Bulíček, Miroslav, Lewandowski, Roger, and Málek, Josef. "On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions." Commentationes Mathematicae Universitatis Carolinae 52.1 (2011): 89-114. <http://eudml.org/doc/246630>.

@article{Bulíček2011,
abstract = {In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity $\nu $ polynomially increasing with a scalar quantity $k$ that evolves according to an evolutionary convection diffusion equation with the right hand side $\nu (k)|\{\mathsf \{D\}\}(\vec\{v\})|^2$ that is merely $L^1$-integrable over space and time. We also formulate a conjecture concerning regularity of such a solution.},
author = {Bulíček, Miroslav, Lewandowski, Roger, Málek, Josef},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {large data existence; suitable weak solution; Navier-Stokes-Fourier equations; incompressible fluid; the viscosity increasing with a scalar quantity; regularity; turbulent kinetic energy model; large data existence; suitable weak solution; Navier-Stokes-Fourier equations; incompressible fluid; the viscosity increasing with a scalar quantity; turbulent kinetic energy model},
language = {eng},
number = {1},
pages = {89-114},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions},
url = {http://eudml.org/doc/246630},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Bulíček, Miroslav
AU - Lewandowski, Roger
AU - Málek, Josef
TI - On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 1
SP - 89
EP - 114
AB - In this paper, we establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity $\nu $ polynomially increasing with a scalar quantity $k$ that evolves according to an evolutionary convection diffusion equation with the right hand side $\nu (k)|{\mathsf {D}}(\vec{v})|^2$ that is merely $L^1$-integrable over space and time. We also formulate a conjecture concerning regularity of such a solution.
LA - eng
KW - large data existence; suitable weak solution; Navier-Stokes-Fourier equations; incompressible fluid; the viscosity increasing with a scalar quantity; regularity; turbulent kinetic energy model; large data existence; suitable weak solution; Navier-Stokes-Fourier equations; incompressible fluid; the viscosity increasing with a scalar quantity; turbulent kinetic energy model
UR - http://eudml.org/doc/246630
ER -

References

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