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Vanishing capillarity limit of the Navier-Stokes-Korteweg system in one dimension with degenerate viscosity coefficient and discontinuous initial density
Cosmin Burtea, Boris Haspot
In the first main result of this paper we prove that one can approximate discontinious solutions of the 1d Navier Stokes system with solutions of the 1d Navier-Stokes-Korteweg syst…
Physical Relaxation Terms for Compressible Two-Phase Systems
Didier Bresch, Cosmin Burtea, Frédéric Lagoutière
In this note, we propose the first mathematical derivation of a macroscopic Baer-Nunziato type system for compressible two-phase flows allowing two pressure state laws depending on…
Weak Solutions for the Stationary Anisotropic and Nonlocal Compressible Navier-Stokes System
D. Bresch, Cosmin Burtea
In this paper, we prove global existence of weak solutions for the stationary compressible Navier-Stokes equations with an anisotropic and nonlocal viscous term in a periodic domai…
New effective pressure and existence of global strong solution for compressible Navier-Stokes equations with general viscosity coefficient in one dimension
Cosmin Burtea, Boris Haspot
In this paper we prove the existence of global strong solution for the Navier-Stokes equations with general degenerate viscosity coefficients. The cornerstone of the proof is the i…
Long time existence results for bore-type initial data for BBM-Boussinesq systems
Cosmin Burtea
In this paper we deal with the long time existence for the Cauchy problem associated to BBM-type Boussinesq systems of equations which are asymptotic models for long wave, small am…