Finite Energy Global Solutions to a Two-fluid Model Arising in Superfluidity
by Paolo Antonelli   Pierangelo Marcati  

Vol. 10 No. 3 (2015) P.349~P.373

ABSTRACT

In this paper we study a hydrodynamic system describing two interacting fluids, which can be seen as a toy model to start an investigation on the so called two-fluid models arising in superfluidity and Bose-Einstein condensates at finite temperatures. We show global existence of finite energy weak solutions, by using a fractional step argument which combines the study of a Cauchy problem for an appropriate nonlinear Schrödinger equation and the polar factorisation techinque. The convergence of the sequence of approximate solutions is then proved by using the dispersive properties of the nonlinear Schrödinger equation.

KEYWORDS
Quantum Hydrodynamics, Two- uid models, Superfluidity.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35Q40, 35Q55, 76Y05.

MILESTONES

Received: 2015-04-10
Revised : 2015-05-29
Accepted: 2015-05-15

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