Uniqueness of Solutions for Zakharov Systems
نویسندگان
چکیده
We prove that the weak solution of the Cauchy problem for the KleinGordon-Zakharov system and for the Zakharov system is unique in the energy space for the former system, and in H×L for the latter system, in dimensions three or lower. These are the largest Sobolev spaces (in three dimensional case) where the local wellposedness has been proven so far. Our proof uses an infinite iteration, where the solution is fixed but the function spaces are converging to the desired ones in the limit.
منابع مشابه
Energy convergence for singular limits of Zakharov type systems
We prove existence and uniqueness of solutions to the Klein-Gordon-Zakharov system in the energy space H × L on some time interval which is uniform with respect to two large parameters c and α. These two parameter correspond to the plasma frequency and the sound speed. In the simultaneous high-frequency and subsonic limit, we recover the nonlinear Schrödinger system at the limit. We are also ab...
متن کاملRegularity Properties of the Zakharov System on the Half Line
In this paper we study the local and global regularity properties of the Zakharov system on the half line with rough initial data. These properties include local and global wellposedness results, local and global smoothing results and the behavior of higher order Sobolev norms of the solutions. Smoothing means that the nonlinear part of the solution on the half line is smoother than the initial...
متن کاملSolitons And Periodic Solutions To The Generalized Zakharov-Kuznetsov Benjamin-Bona-Mahoney Equation
This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...
متن کاملMartingale and Pathwise Solutions to the Stochastic Zakharov-kuznetsov Equation with Multiplicative Noise
We study in this article the stochastic Zakharov-Kuznetsov equation driven by a multiplicative noise. We establish, in space dimensions two and three the global existence of martingale solutions, and in space dimension two the global pathwise uniqueness and the existence of pathwise solutions. New methods are employed to deal with a special type of boundary conditions and to verify the pathwise...
متن کاملSolution of the fractional Zakharov-Kuznetsov equations by reduced dierential transform method
In this paper an approximate analytical solution of the fractional Zakharov-Kuznetsov equations will be obtained with the help of the reduced differential transform method (RDTM). It is in-dicated that the solutions obtained by the RDTM are reliable and present an effective method for strongly nonlinear fractional partial differential equations.
متن کامل