Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. Part II

AbstractWe consider the Zakharov equation in space dimension two $$\left\{ {\begin{array}{*{20}c} {iu_t = - \Delta u + nu,} \\ {\frac{1}{{c_0^2 }}n_{tt} = \Delta n + \Delta \left| u \right|^2 } \\ \end{array} } \right.$$ .In the first part of the paper, we consider blow-up solutions of this equation. We prove various concentration properties of these solutions: existence, characterization of concentration mass, non existence of minimal concentration mass.In the second part, we prove instability of periodic solutions.

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