Speaker: 赖善发，澳门大学

Inviter: 王和明

Title: Planar Gross-Pitaevskii Traveling Waves at Every Subsonic Speed

Language: Chinese

Time & Venue: 2026.10.16 10:00-11:00 思源楼S713

Abstract: The Gross-Pitaevskii equation is an important model for superfluidity and Bose–Einstein condensates. In this talk, we study finite-energy traveling waves for this equation in the plane. We prove that a nonconstant finite-energy traveling wave exists for every prescribed subsonic speed \(c\in(0,\sqrt{2})\), resolving the longstanding prescribed-speed existence problem in two dimensions. The key is an a priori estimate that controls the energy by the action and the Morse index, without additional assumptions on the number, degrees, or locations of the zeros. We also establish finite-bubble compactness, including splitting of the energy, action, potential energy, and momentum, and prove that the least action is attained among nonconstant finite-energy waves of Morse index at most one. We will discuss the background, the main results, and the key ideas of the proofs.