Global strong solutions exist and are unique for 1D compressible NS/CH with vacuum without compatibility conditions via singular-in-time weighted estimates.
Local-in-time existence of strong solutions to a quasi-incompressible Cahn--Hilliard--Navier--Stokes system
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abstract
We analyze a quasi-incompressible Cahn--Hilliard--Navier--Stokes system (qCHNS) for two-phase flows with unmatched densities. The order parameter is the volume fraction difference of the two fluids, while mass-averaged velocity is adopted. This leads to a quasi-incompressible model where the pressure also enters the equation of the chemical potential. We establish local existence and uniqueness of strong solutions by the Banach fixed point theorem and the maximal regularity theory.
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2026 1verdicts
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Global strong solutions for 1D compressible Navier-Stokes/Cahn-Hilliard equations with vacuum
Global strong solutions exist and are unique for 1D compressible NS/CH with vacuum without compatibility conditions via singular-in-time weighted estimates.