Global classical solutions exist for spherically symmetric large initial data in the multi-dimensional compressible Navier-Stokes-Poisson equations on solid balls with BD-type viscosity coefficients.
Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
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abstract
This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the energy inequality, the BD entropy one, and the Mellet-Vasseur type estimate. Then, after adapting the compactness results due to Mellet-Vasseur [Comm. Partial Differential Equations 32 (2007)], we obtain the global existence of weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in two or three dimensional periodic domains or whole space for large initial data. This, in particular, solved an open problem in [P. L. Lions. Mathematical topics in fluid mechanics. Vol. 2. Compressible models. Oxford University Press, 1998].
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UNVERDICTED 6representative citing papers
Global well-posedness of regular solutions to barotropic compressible Navier-Stokes with density-dependent viscosities ρ^δ (δ ∈ (1/2,1)) for large spherical symmetric data vanishing at infinity in 2 and 3 dimensions.
Global regular solutions exist for the degenerate compressible Navier-Stokes equations with large spherically symmetric initial data, preventing singularities for gamma in (1, infinity) in 2D and (1,3) in 3D.
Global strong solutions exist and are unique for spherically symmetric isothermal compressible Navier-Stokes with far-field vacuum when δ > 0.7427, removing the γ-δ-1/p restriction.
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.
Global well-posedness of spherically symmetric classical solutions is established for degenerate compressible Navier-Stokes equations in 2D and 3D with large initial data for alpha above approximately 0.54-0.68 and gamma in specified ranges.
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Global existence of classical solutions for the multi-dimensional compressible Navier-Stokes-Poisson equations on solid balls for arbitrary spherically symmetric large initial data
Global classical solutions exist for spherically symmetric large initial data in the multi-dimensional compressible Navier-Stokes-Poisson equations on solid balls with BD-type viscosity coefficients.
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Global Regular Solutions of the Compressible Navier-Stokes Equations with Nonlinear Density-Dependent Viscosities and Large Initial Data of Spherical Symmetry
Global well-posedness of regular solutions to barotropic compressible Navier-Stokes with density-dependent viscosities ρ^δ (δ ∈ (1/2,1)) for large spherical symmetric data vanishing at infinity in 2 and 3 dimensions.
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Global Regular Solutions of the Degenerate Compressible Navier-Stokes Equations with Large Initial Data of Spherical Symmetry
Global regular solutions exist for the degenerate compressible Navier-Stokes equations with large spherically symmetric initial data, preventing singularities for gamma in (1, infinity) in 2D and (1,3) in 3D.
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Global spherically symmetric solutions to the isothermal compressible Navier-Stokes equations with far-field vacuum
Global strong solutions exist and are unique for spherically symmetric isothermal compressible Navier-Stokes with far-field vacuum when δ > 0.7427, removing the γ-δ-1/p restriction.
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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.
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Global Well-Posedness of Classical Solutions to the Multi-Dimensional Degenerate Compressible Navier-Stokes Equations with Large Spherically Symmetric Initial Data
Global well-posedness of spherically symmetric classical solutions is established for degenerate compressible Navier-Stokes equations in 2D and 3D with large initial data for alpha above approximately 0.54-0.68 and gamma in specified ranges.