F.-H. Lin

Courant Institute

**Semi-Classical Limit of the Gross-Pitaeveskii Equations in an
Exterior Domain**

Courant Institute

Here we discuss the semiclassical limits of the Gross-Pitaeveskii equations(a cubic nonlinear Schrodinger equations) in an exterior domain. The problem is motivated by a study of superfluids passing an obstacle. We shall show under rather natural physical conditions that the quantum density and quantum momentum converge to the density and the momentum of the classical Euler equations when a scaling parameter goes to zero.