3 papers
math.AP2025
Remarks on the derivation of the virial identity for nonlinear Schrödinger equations
Tomoyuki Ikeda, Shuji Machihara, Hayato Miyazaki +1
We revisit the derivation of the virial identity for nonlinear Schrödinger equations. In \cite{O06, FM17}, several conservation laws, such as for the charge and the energy, were de…
math.AP2024
Global existence and blow-up for the variable coefficient Schrödinger equations with a linear potential
Bowen Zheng, Tohru Ozawa
In this paper, we study a class of variable coefficient Schrödinger equations with a linear potential \[i\partial_tu+\nabla\cdot(|x|^b\nabla u)-V(x)u=-|x|^c|u|^pu,\] where $2-n<b\l…
math.AP2024
The blow-up dynamics for the divergence Schrödinger equations with inhomogeneous nonlinearity
Bowen Zheng, Tohru Ozawa
This paper is dedicated to the blow-up solution for the divergence Schrödinger equations with inhomogeneous nonlinearity (dINLS for short) \[i\partial_tu+\nabla\cdot(|x|^b\nabla u)…