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5 papers · 1 filter
Analysis of acoustic oscillations for a class of hydrodynamic systems describing quantum fluids
Paolo Antonelli, Lars Eric Hientzsch, Pierangelo Marcati
Hydrodynamic systems for quantum fluids are systems for compressible fluid flows for which quantum effects are macroscopically relevant. We discuss how the presence of the dispersi…
Global Large Data Solutions of 2D Dirac Equation with Hartree Type Interaction
Vladimir Georgiev, Boris Shakarov
Local and global well - posedness of the solution to the two space dimensional Dirac equation with Hartree type nonlinearity is established with the initial datum in the space $H^s…
Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles
Mingjie Li, Tian-Yi Wang, Wei Xiang
In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is p…
Renormalized solutions to the continuity equation with an integrable damping term
Maria Colombo, Gianluca Crippa, Stefano Spirito
We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions proved that, when the damping term is bounded in…
Renormalized solutions of the 2d Euler equations
Gianluca Crippa, Stefano Spirito
In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.