The paper develops a hierarchy of entropies that propagate smoothness for 1D compressible fluids with degenerate viscosity and alignment, yielding global well-posedness for the pressured Cucker-Smale model.
Existence of global strong solution for the compressible Navier-Stokes equations with degenerate viscosity coefficients in 1D
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abstract
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. We prove the existence of global strong solution with large initial data for the shallow water system. The key ingredient of the proof relies to a new formulation of the compressible equations involving a new effective velocity $v$ (see \cite{cras,para,CPAM,CPAM1}) such that the density verifies a parabolic equation. We estimate $v$ in $L^\infty$ norm which enables us to control the vacuum on the density.
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math.AP 1years
2019 1verdicts
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Entropy Hierarchies for equations of compressible fluids and self-organized dynamics
The paper develops a hierarchy of entropies that propagate smoothness for 1D compressible fluids with degenerate viscosity and alignment, yielding global well-posedness for the pressured Cucker-Smale model.