报告题目：Normalised solutions and limit profiles of the Gross-Pitaevskii-Poisson equation

报告人：Vitaly Moroz, Swansea University

报告时间：2023年12月19日（周二）14:00-15:00

报告地点：20-308

报告摘要：Gross-Pitaevskii-Poisson (GPP) equation is a nonlocal modification of the Gross-Pitaevskii equation with an attractive Coulomb-like term. It appears in the models of self-gravitating Bose-Einstein condensates proposed in cosmology and astrophysics to describe Cold Dark Matter and Boson Stars. We investigate the existence of prescribed mass (normalised) solutions to the GPP equation, paying special attention to the shape and asymptotic behaviour of the associated mass-energy relation curves and to the limit profiles of solutions at the endpoints of these curves. In particular, we show that after appropriate rescalings, the constructed normalized solutions converge either to a ground state of the Choquard equation, or to a compactly supported radial ground state of the integral Thomas-Fermi equation. In different regimes the constructed solutions include global minima, local but not global minima and unstable mountain-pass type solutions. This is a joint work with Riccardo Molle and Giuseppe Riey.

报告人简介：Vitaly Moroz is a Professor at Mathematics Department, Swansea University. His research is in the Analysis of Nonlinear Partial Differential Equations (PDEs). It is focussed on the fundamental questions of existence, non-existence, and structure of solution sets of nonlinear elliptic equations and inequalities. Recently he was mostly working on nonlinear Schrödinger type equations with nonlocal interactions, such as Choquard-Pekar (Schrödinger-Newton) equations, Schrödinger-Poisson type equations, nonlocal Hartree type equations arising in the density functional theory models for graphene. The common mathematical feature of all these models is that, unlike in the case of classical local PDEs, nonlocal terms are present in the equations via Coulombian type interactions or via a fractional Laplacian term, or both. The tools employed are from the Calculus of Variations, elliptic PDEs theory and Potential Theory.

邀请人：非线性分析与PDE团队