no code implementations • 28 Dec 2020 • Baoping Liu, Avy Soffer
We give a short description of the proof of asymptotic-completeness for NLS-type equations, including time dependent potential terms, with radial data in three dimensions.
Analysis of PDEs Mathematical Physics Mathematical Physics 35P25, 35Q55, 47A40
no code implementations • 28 Dec 2020 • Avy Soffer
I describe a way to modify the multipliers of a-priori estimates, so as to include potential perturbations of the Laplacian.
Analysis of PDEs 35P15
no code implementations • 28 Dec 2020 • Avy Soffer, Xiaoxu Wu
This paper establishes the $L^p$ boundedness of wave operators for linear Schr\"odinger equations in $\mathbb{R}^3$ with time-dependent potentials.
Analysis of PDEs 35P25, 35Q55, 47A40
no code implementations • 28 Dec 2020 • Avy Soffer, Yifei Wu, Xiaohua Yao
In this paper, we consider the global Cauchy problem for the $L^2$-critical semilinear heat equations $ \partial_t h=\Delta h\pm |h|^{\frac4d}h, $ with $h(0, x)=h_0$, where $h$ is an unknown real function defined on $ \R^+\times\R^d$.
Analysis of PDEs 35K05, 35B40, 35B65