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Davey-Stewartson equation generalized: global existence vs. blow-up of solutions
Alp Eden
Date: Monday, November 19, 2007 In this talk I will review some of the work done jointly with C. Babaoglu, S. Erbay, H. Erbay, G. Muslu, I. A. Topaloglu and E. Kuz on the generalized Davey-Stewartson equations in the purely elliptic case. I will cast these equations as a Nonlinear Schroedinger Equation (NLS) with cubic like non-local non-linearity in 2D and discuss some of the conserved quantities and their relation to the global existence of solutions; virial identity and its relation with blow-up of solutions; the pseudoconformal invariance and its relation with the time asymptotics of solutions. I will also review the on-going work on the existence and uniqueness of solutions for NLS equations with non-local terms on various Sobolev spaces in the spirit of Kato's [1987] work for NLS. |