Existence of invariant measures and Feller property of the Markov semigroup are established for 1D stochastic compressible Navier-Stokes equations with Korteweg capillarity.
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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 strong solutions to the compressible NSK system exist in R^2 and R^3 for arbitrarily large initial data with non-vacuum far-field density.
citing papers explorer
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Invariant measures for the one-dimensional stochastic Navier-Stokes-Korteweg equations
Existence of invariant measures and Feller property of the Markov semigroup are established for 1D stochastic compressible Navier-Stokes equations with Korteweg capillarity.
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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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On the Cauchy problem for the multi-dimensional compressible Navier-Stokes-Korteweg system: Global strong solutions with arbitrarily large initial data
Global strong solutions to the compressible NSK system exist in R^2 and R^3 for arbitrarily large initial data with non-vacuum far-field density.