Invariant measures and global well-posedness for a fractional Schrödinger equation with Moser-Trudinger type nonlinearity
Invariant measures and global well-posedness for a fractional Schrödinger equation with Moser-Trudinger type nonlinearity
Abstract In this paper, we construct invariant measures and global-in-time solutions for a fractional Schrödinger equation with a Moser–Trudinger type nonlinearity $$\begin{aligned} i\partial _t u= (-\Delta )^{\alpha }u+ 2\beta u e^{\beta |u|^2} \qquad \text{ for }\qquad (x,t)\in \ M\times \mathbb {R}\end{aligned}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mtable> <mml:mtr> <mml:mtd> <mml:mrow> <mml:mi>i</mml:mi> <mml:msub> …