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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, Staffilani, Takaoka and Tao. A polynomial growth bound for the solution is also given.
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 ener
Existence and uniqueness of solutions to the Navier-Stokes equation in dimension two with forces in the space $L^q( (0,T); mathbf{W}^{-1,p}(Omega))$ for $p$ and $q$ in appropriate parameter ranges are proven. The case of spatially measured-valued inh
In this paper, we consider the three-dimensional full compressible viscous non-resistive MHD system. Global well-posedness is proved for an initial-boundary value problem around a strong background magnetic field. It is also shown that the unique sol
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such solutions have
We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form $u_ito partial_tu_i-Delta(a_i(tilde{u})u_i)$ where the $u_i, i=1,...,I$ represent $I$ density-functions, $tilde