Title: Global well-posedness for the nonlinear Schrodinger equation with derivative in energy space
报告人: 吴奕飞 研究员 (北京师范大学)
时间: 3月22日 星期五 10:00-11:30
地点: 理科一号楼1569
摘要： In this short paper, we prove that there exists some small $\varepsilon_*>0$, such that the derivative nonlinear Schr\"{o}dinger equation (DNLS) is global well-posedness in the energy space, provided that the initial data $u_0\in H^1$ with $\|u_0\|_{L^2}<\sqrt{2\pi}+\varepsilon_*$. This result shows us that there are no blow up solutions whose mass are close to $2\pi$, even if the energies of them are negative (different from power-type nonlinear Schr\"odinger equation). The technique to prove the main theorem is some variational argument, together with the momentum conservation laws. Further, we show that for the DNLS on the half line, the phenomena is different, and the blowup occurs for the solution with negative energy.