EXISTENCE AND UNIQUENESS OF MINIMAL BLOW-UP SOLUTIONS TO AN INHOMOGENEOUS MASS CRITICAL NLS

摘要

We deal in this paper with a two-dimensional focusing mass critical nonlinear Schrodinger equation with an inhomogeneous nonlinearity: ia_tu = -Δu — k(x)|u|~2u, (t, x) ∑ R x R~2, (1.1)(NLS) u(to, x) =no (x), u0 : R~2C, for some smooth bounded inhomogeneity k : R~2 —> R~*_+ and some real number to < 0. This kind of problem arises naturally in nonlinear optics for the propagation of laser beams. From the mathematical point of view, it is a canonical model to break the large group of symmetries of the k 1 homogeneous case.