Global weak solutions exist for the chemotaxis compressible Navier-Stokes system with density-dependent viscosity on the 3D torus for adiabatic exponents γ > 4/3 and energy-finite initial data.
Feireisl.Dynamics of Viscous Compressible Fluids
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Chemotaxis compressible Navier-Stokes equations with density-dependent viscosity modeling vascular network formation
Global weak solutions exist for the chemotaxis compressible Navier-Stokes system with density-dependent viscosity on the 3D torus for adiabatic exponents γ > 4/3 and energy-finite initial data.