【摘 要】
：
In this paper,we consider in Rn the Cauchy problem for nonlinear Schr(o)dinger equation with initial data in Sobolev space Ws,p for p < 2.It iswell known th
【机 构】
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FudanUniversity,Shanghai,China
【出 处】
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International Conference on Nonlinear PDEs and Their Applica
论文部分内容阅读
In this paper,we consider in Rn the Cauchy problem for nonlinear Schr(o)dinger equation with initial data in Sobolev space Ws,p for p < 2.It iswell known that this problem is ill posed.However,We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in Ws,p for 2n/n+1 < p < 2 and s > n(1-1/p).Moreover,we show that in one space dimension,the problem is locally well posed in Lp for any 1 < p < 2.
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