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On dyadic nonlocal Schr鰀inger equations with Besov initial data
Schrodinger equation Besov spaces Haar bases Nonlocal derivatives
2012/6/21
In this paper we characterize a dyadic type Besov space as an adequate setting to solve the Schr\"{o}dinger-Dirac type equation $i\tfrac{\partial u}{\partial t}=D^{\beta}u$ with $u(x,0)=u^0$ pointwise...
Cauchy problem of nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2
Applied mathematics Cauchy problem nonlinear Schrodinger equation local well-posedness scaling limit
2011/10/15
In this paper, we consider in R^n the Cauchy problem for nonlinear Schrodinger equation with initial data in Sobolev space W^{s,p} for p<2. It is well known that this problem is ill posed. However, We...
Global Existence of Solutions for the Cauahy Problem of the Kawahara Equation with $L^2$ Initial Data
Kawahara equation Cauchy problem global solution
2007/12/11
In this paper we study solvability of the Cauchy problem of the Kawahara equation $\partial_tu+au\partial_xu+\beta\partial^3_xu+\gamma\partial^5_xu =0$ with $L^2$ initial data. By working on the Bourg...