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The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are proved, including the case of initial data in the energy space. None of these results is restricted to radially symmetric data.
The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L^2 - norm of the Schrodinger part is small enough. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffi
We prove small energy scattering for the 3D Zakharov system with radial symmetry. The main ingredients are normal form reduction and the radial-improved Strichartz estimates.
In this paper we study the Cauchy problem for the elliptic and non-elliptic derivative nonlinear Schrodinger equations in higher spatial dimensions ($ngeq 2$) and some global well-posedness results with small initial data in critical Besov spaces $B^
The initial value problem for the $L^{2}$ critical semilinear Schrodinger equation in $R^n, n geq 3$ is considered. We show that the problem is globally well posed in $H^{s}({Bbb R^{n}})$ when $1>s>frac{sqrt{7}-1}{3}$ for $n=3$, and when $1>s> frac{-
We consider the stochastic electrokinetic flow in a smooth bounded domain $mathcal{D}$, modelled by a Nernst-Planck-Navier-Stokes system with a blocking boundary conditions for ionic species concentrations, perturbed by multiplicative noise. Several