Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions
Journées équations aux dérivées partielles (2001), article no. 7, 9 p.

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.

@article{JEDP_2001____A7_0,
     author = {Hoff, David},
     title = {Dynamics of {Singularity} {Surfaces} for {Compressible} {Navier-Stokes} {Flows} in {Two} {Space} {Dimensions}},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {7},
     publisher = {Universit\'e de Nantes},
     year = {2001},
     doi = {10.5802/jedp.591},
     zbl = {1005.35075},
     mrnumber = {1843408},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/jedp.591/}
}
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
DA  - 2001///
PB  - Université de Nantes
UR  - http://archive.numdam.org/articles/10.5802/jedp.591/
UR  - https://zbmath.org/?q=an%3A1005.35075
UR  - https://www.ams.org/mathscinet-getitem?mr=1843408
UR  - https://doi.org/10.5802/jedp.591
DO  - 10.5802/jedp.591
LA  - en
ID  - JEDP_2001____A7_0
ER  - 
%0 Journal Article
%A Hoff, David
%T Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions
%J Journées équations aux dérivées partielles
%D 2001
%I Université de Nantes
%U https://doi.org/10.5802/jedp.591
%R 10.5802/jedp.591
%G en
%F JEDP_2001____A7_0
Hoff, David. Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. Journées équations aux dérivées partielles (2001), article  no. 7, 9 p. doi : 10.5802/jedp.591. http://archive.numdam.org/articles/10.5802/jedp.591/

[1] P. Duhem Recherches sur l'hydrodynamique Ann. Toulouse 2 1901-03. | JFM | Numdam

[2] Eduard Feireisl Global attractors for the Navier-Stokes equations of three-dimensional compressible flow to appear. | MR

[3] David Hoff Global solutions of the Navier-Stokes equations for multidimensional, compressible flow with discontinuous initial data, J. Diff. Eqns. 120, no. 1 1995, 215-254. | MR | Zbl

[4] David Hoff Strong 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. | MR | Zbl

[5] David Hoff Discontinuous solutions of the Navier-Stokes equations for multidimensional, heat conducting flow Archive Rational Mech. Ana. 139 1997, 303-354. | MR | Zbl

[6] David Hoff Dynamics of Singularity Surfaces for Solutions of the Navier-Stokes Equations of Compressible Flow in Two Space Dimensions in preparation.

[7] David Hoff and Mohammed Ziane Compact attractors for the Navier-Stokes equations of one dimensional, compressible flow C.R. Acad. Sci. Série I 1999, 239-244. | MR | Zbl

[8] David Hoff and Mohammed Ziane The 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. | MR | Zbl

[9] Denis Serre Variations de grande amplitude pour la densite d'un fluide visqueux compressible Physica D 48 1991, 113-128. | MR | Zbl

Cited by Sources: