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 = {David Hoff},
     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 = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.591/}
}
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David Hoff. 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. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.591/

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