On the local well-posedness for the nonlinear Schrödinger equation with spatial variable coefficient

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• 作者：Jian Zhai ; Bowen Zheng ; ^{bwen_zj1516@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Schrö ; dinger equation with spatial variable coefficient ; Strichartz estimate ; Well-posedness
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 January 2017
• 年：2017
• 卷：445
• 期：1
• 页码：81-96
• 全文大小：414 K

文摘

We study a new type of nonlinear Schrödinger equation where the coefficient of Laplacian depends on spatial variable. Based on a modified Hankel transform and delicate frequency estimates, we establish the local well-posedness of the NLS with spatial variable coefficient in the weighted Lebesgue space for n&ge;2$n\&<font\; color="red">ge</font>;2$, and extend the Strichartz estimates to the non-radially Schrödinger equation with spatial variable coefficient in 2D Euclidian space.