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- W3123670220 abstract "In this paper, we consider the following inhomogeneous nonlinear Schrodinger equation (INLS) $$$ipartial_t u + Delta u + mu$$$ |$$$x$$$|$$$^{-b}$$$|$$$u$$$|$$$^alpha u = 0, quad (t,x)in ℝ times ℝ^d$$$ with $$$b, alpha$$$ > 0. First, we revisit the local well-posedness in $$$H^1(ℝ^d)$$$ for (INLS) of Guzman [Nonlinear Anal. Real World Appl. 37 (2017), 249-286] and give an improvement of this result in the two and three spatial dimensional cases. Second, we study the decay of global solutions for the defocusing (INLS), i.e. $$$mu=-1$$$ when 0 < $$$alpha$$$ < $$$alpha^star$$$ where $$$alpha^star = frac{4-2b}{d-2}$$$ for $$$dgeq 3$$$, and $$$alpha^star = infty$$$ for $$$d=1, 2$$$ by assuming that the initial data belongs to the weighted $$$L^2$$$ space $$$Sigma ={u in H^1(ℝ^d) :$$$ |$$$x$$$|$$$ u in L^2(ℝ^d) }$$$. Finally, we combine the local theory and the decaying property to show the scattering in $$$Sigma$$$ for the defocusing (INLS) in the case $$$alpha_star$$$ < $$$alpha$$$ < $$$alpha^star$$$, where $$$alpha_star = frac{4-2b}{d}$$$." @default.
- W3123670220 created "2021-02-01" @default.
- W3123670220 creator A5087338257 @default.
- W3123670220 date "2020-09-21" @default.
- W3123670220 modified "2023-09-27" @default.
- W3123670220 title "[Forthcoming] Théorie de diffusion dans les espaces L2 pondérés pour une classe de l'équation de Schrödinger non-linéaire inhomogène défocalisée" @default.
- W3123670220 hasPublicationYear "2020" @default.
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