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Register a new userScattering for the non-radial inhomogeneous NLS
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We extend the result of Farah and Guzman on scattering for the $3d$ cubic inhomogeneous NLS to the non-radial setting. The key new ingredient is a construction of scattering solutions corresponding to initial data living far from the origin.
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We prove scattering below the ground state threshold for an energy-critical inhomogeneous nonlinear Schrodinger equation in three space dimensions. In particular, we extend results of Cho, Hong, and Lee from the radial to the non-radial setting.
In this paper, we study the long-time behavior of global solutions to the Schrodinger-Choquard equation $$ipartial_tu+Delta u=-(I_alphaast|cdot|^b|u|^{p})|cdot|^b|u|^{p-2}u.$$ Inspired by Murphy, who gave a simple proof of scattering for the non-radial inhomogeneous NLS, we prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.
We adapt the argument of Dodson-Murphy to give a simple proof of scattering below the ground state for the intercritical inhomogeneous nonlinear Schrodinger equation. The decaying factor in the nonlinearity obviates the need for a radial assumption.
In this paper, we study the scattering theory for the cubic inhomogeneous Schrodinger equations with inverse square potential $iu_t+Delta u-frac{a}{|x|^2}u=lambda |x|^{-b}|u|^2u$ with $a>-frac14$ and $0<b<1$ in dimension three. In the defocusing case (i.e. $lambda=1$), we establish the global well-posedness and scattering for any initial data in the energy space $H^1_a(mathbb R^3)$. While for the focusing case(i.e. $lambda=-1$), we obtain the scattering for the initial data below the threshold of the ground state, by making use of the virial/Morawetz argument as in Dodson-Murphy [Proc. Amer. Math. Soc.,145(2017), 4859-4867.] and Campos-Cardoso [arXiv: 2101.08770v1.] that avoids the use of interaction Morawetz estimate.
In this paper, we give a simple proof of scattering result for the Schrodinger equation with combined term $ipa_tu+Delta u=|u|^2u-|u|^4u$ in dimension three, that avoids the concentrate compactness method. The main new ingredient is to extend the scattering criterion to energy-critical.
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