Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions

David Hoff

Journées équations aux dérivées partielles (2001)

  • page 1-9
  • ISSN: 0752-0360

Abstract

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We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller viscosities.

How to cite

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Hoff, David. "Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions." Journées équations aux dérivées partielles (2001): 1-9. <http://eudml.org/doc/93418>.

@article{Hoff2001,
abstract = {We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller viscosities.},
author = {Hoff, David},
journal = {Journées équations aux dérivées partielles},
keywords = {global existence; Navier-Stokes equations; compressible, barotropic flow; piecewise smooth initial data},
language = {eng},
pages = {1-9},
publisher = {Université de Nantes},
title = {Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions},
url = {http://eudml.org/doc/93418},
year = {2001},
}

TY - JOUR
AU - Hoff, David
TI - Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions
JO - Journées équations aux dérivées partielles
PY - 2001
PB - Université de Nantes
SP - 1
EP - 9
AB - We prove the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time, more rapidly for larger acoustic speeds and smaller viscosities.
LA - eng
KW - global existence; Navier-Stokes equations; compressible, barotropic flow; piecewise smooth initial data
UR - http://eudml.org/doc/93418
ER -

References

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  1. [1] P. DuhemRecherches sur l'hydrodynamique Ann. Toulouse 2 1901-03. JFM34.0795.02
  2. [2] Eduard FeireislGlobal attractors for the Navier-Stokes equations of three-dimensional compressible flow to appear. MR1780182
  3. [3] David HoffGlobal solutions of the Navier-Stokes equations for multidimensional, compressible flow with discontinuous initial data, J. Diff. Eqns. 120, no. 1 1995, 215-254. Zbl0836.35120MR1339675
  4. [4] David HoffStrong convergence to global solutions for compressible viscous, multidimensional flow, with polytropic equations of state and discontinuous initial data Arch. Rational Mech. Ana. 132 1995, 1-14. Zbl0836.76082MR1360077
  5. [5] David HoffDiscontinuous solutions of the Navier-Stokes equations for multidimensional, heat conducting flow Archive Rational Mech. Ana. 139 1997, 303-354. Zbl0904.76074MR1480244
  6. [6] David HoffDynamics of Singularity Surfaces for Solutions of the Navier-Stokes Equations of Compressible Flow in Two Space Dimensions in preparation. 
  7. [7] David Hoff and Mohammed ZianeCompact attractors for the Navier-Stokes equations of one dimensional, compressible flow C.R. Acad. Sci. Série I 1999, 239-244. Zbl0926.35113MR1674555
  8. [8] David Hoff and Mohammed ZianeThe global attractor and finite determining nodes for the Navier-Stokes equations of compressible flow with singular initial data Indiana Univ. Math. J. 49, no. 3 ( 2000), 843-889. Zbl0977.35105MR1803214
  9. [9] Denis SerreVariations de grande amplitude pour la densite d'un fluide visqueux compressible Physica D 48 1991, 113-128. Zbl0739.35071MR1098658

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