Eliott Kacedan, Kohei Soga
Published 2023-03-15Version 1
This paper proves existence of a global weak solution of the inhomogeneous (i.e., non-constant density) incompressible Navier-Stokes system with mass diffusion. The system is well-known as the Kazhikhov-Smagulov model. The major novelty of the paper is to deal with the Kazhikhov-Smagulov model possessing the non-constant viscosity without any simplification of higher order nonlinearity. Any global weak solution is shown to have a long time behavior that is consistent with mixing phenomena of miscible fluids. The results also contain a new compactness method of the Aubin-Lions-Simon type.
On the nonexistence of global weak solutions to the Navier-Stokes-Poisson equations in $\Bbb R^N$
Well-posedness and long time behavior in nonlinear dissipative hyperbolic-like evolutions with critical exponents
Global weak solutions for a periodic two-component $μ$-Hunter-Saxton system
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