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Dynamics of singularity surfaces for compressible Navier-Stokes flows in two space dimensions. (English) Zbl 1005.35075
Journées “Équations aux dérivées partielles”, Plestin-les-Grèves, France, 5 au 8 juin 2001. Exposés Nos. I-XIV. Nantes: Université de Nantes. Exp. No. 7, 9 p. (2001).
Summary: 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.
For the entire collection see [Zbl 0990.00046].
MSC:
35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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