Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
Dispersive equations are useful for describing a wide variety of phenomena in which solutions disperse through the space as time progresses. These equations show up frequently in physics, especially when studying quantum mechanical and fluid related systems. The single particle variants of equations such as the Schr\"{o}dinger and Wave equations have been studied at great length throughout modern history. Over the last couple decades progress has been made toward extending single particle dispersive equations to cover their many body counterparts. Space-time Strichartz estimates for the homogenous $N$-particle Schr\"{o}dinger equation with small interacting potentials was recently established on both $\mathbb{R}^d$ and $\mathbb{T}^d$ ( see \cite{HONG}, \cite{HUANG}). We look to extend upon this and establish Strichartz estimates for an $N$-body extension of the wave equation with small interacting potentials. In order to achieve this in standard mixed Lebesgue spaces, $L^p_tL^q_x$, we utilize wave-adapted versions of bounded $p$-Variation spaces $V^p$ and their close cousin the atomic space $U^q$.
Date
7-9-2025
Recommended Citation
Reynoso, Tristan, "Strichartz Estimates for Many Particle Dispersive Equations" (2025). LSU Doctoral Dissertations. 6848.
https://repository.lsu.edu/gradschool_dissertations/6848
Committee Chair
Bulut, Aynur
DOI
10.31390/gradschool_dissertations.6848