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 glob al weak solutions for a 2d viscous shallow water equations an d convergence to the quasi-geostrophic model
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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.