TY - ELEC
AU - Yanxia Deng
PY - 2019
TI - A PDE approach to the N-body problem with strong force
LA - eng
M3 - Moving Image
AB - In a joint work with S. Ibrahim, we use the idea of ground states and excited states in nonlinear dispersive equations (e.g. Klein-Gordon and Schr\"odinger equations) to characterize solutions in the N-body problem with strong force under some energy constraints. Indeed, relative equilibria of the N-body problem play a similar role as solitons in PDE. I will introduce the ground state and excited energy for the general N-body problem and give a conditional dichotomy of the global existence and singularity below the excited energy. This dichotomy is given by the sign of a threshold function. I will also talk about a restricted 3-body problem (Hill's lunar type problem) that has a very nice analogy to the nine-set theorem studied by Nakanishi-Schlag on NLKG.
N2 - In a joint work with S. Ibrahim, we use the idea of ground states and excited states in nonlinear dispersive equations (e.g. Klein-Gordon and Schr\"odinger equations) to characterize solutions in the N-body problem with strong force under some energy constraints. Indeed, relative equilibria of the N-body problem play a similar role as solitons in PDE. I will introduce the ground state and excited energy for the general N-body problem and give a conditional dichotomy of the global existence and singularity below the excited energy. This dichotomy is given by the sign of a threshold function. I will also talk about a restricted 3-body problem (Hill's lunar type problem) that has a very nice analogy to the nine-set theorem studied by Nakanishi-Schlag on NLKG.
UR - https://open.library.ubc.ca/collections/48630/items/1.0387390
ER - End of Reference