About the barotropic compressible quantum Navier-Stokes equations

Marguerite Gisclon (1) , Ingrid Lacroix-Violet (2)

1 LAMA - Laboratoire de Mathématiques
2 RAPSODI - Reliable numerical approximations of dissipative systems

In this paper we consider the barotropic compressible quantum Navier-Stokes equations with a linear density dependent viscosity and its limit when the scaled Planck constant vanish. Following recent works on degenerate compressible Navier-Stokes equations, we prove the global existence of weak solutions by the use of a singular pressure close to vacuum. With such singular pressure, we can use the standard definition of global weak solutions which also allows to justify the limit when the scaled Planck constant denoted by ε tends to 0.

Mots clés: asymptotic analysis; global weak solutions; Quantum Navier-Stokes equations

Domaines: Equations aux dérivées partielles [math.AP]

Marguerite Gisclon, Ingrid Lacroix-Violet. About the barotropic compressible quantum Navier-Stokes equations. Nonlinear Analysis: Theory, Methods and Applications, 2015, 128, pp.106-121. ⟨10.1016/j.na.2015.07.006⟩. ⟨hal-01090191⟩