关于勉强\dot{H}^{s_{p}}超临界Wave Equations的一点注记
One Remark on Barely \dot{H}^{s_{p}} Supercritical Wave Equations
摘要：
证明了三维波动方程\partial_{tt} u - \triangle u = - |u| ^{p-1} u的一个好的\dot{H}^{s_{p}}临界理论可以推广到至少一个三维刚\dot{H}^{s_{p}}超临界波动方程\partial_{tt} u - \triangle u =- |u| ^{p-1} u g的光滑解的整体适定性（|u|），其中g缓慢增长到无穷大，只要满足Kenig-Merle型条件。该结果扩展了对于s_{p} =1的特定情况所获得的结果。
英文摘要：
We prove that a good \dot{H}^{s_{p}} critical theory for the 3D wave equation \partial_{tt} u - \triangle u = -|u|^{p-1} u can be extended to prove global well-posedness of smooth solutions of at least one 3D barely \dot{H}^{s_{p}} supercritical wave equation \partial_{tt} u - \triangle u =- |u|^{p-1} u g(|u|), with g growing slowly to infinity, provided that a Kenig-Merle type condition is satisfied. This result extends those obtained for the particular case s_{p}=1.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
