Publications (7)
Solutions to a two-dimensional, Neumann free boundary problem
Sarah Raynor, John A. Gemmer, Gary Moon
We explore regularity properties of solutions to a two-phase elliptic free boundary problem near a Neumann fixed boundary in two dimensions. Consider a function u, which is harmoni…
Dynamics near a minimal-mass soliton for a Korteweg-de Vries equation
Jeremy L. Marzuola, Sarah Raynor, Gideon Simpson
We study soliton solutions to a generalized Korteweg - de Vries (KdV) equation with a saturated nonlinearity, following the line of inquiry of the authors for the nonlinear Schröd…
Asymptotic Stability for KdV Solitons in Weighted Spaces via Iteration
Brian Pigott, Sarah Raynor
In this paper, we reconsider the well-known result of Pego-Weinstein \cite{MR1289328} that soliton solutions to the Korteweg-deVries equation are asymptotically stable in exponenti…
Ground state mass concentration in the L^2-critical nonlinear Schrodinger equation below H^1
Jim Colliander, Sarah Raynor, Catherine Sulem +1
We consider finite time blowup solutions of the -critical cubic focusing nonlinear Schrödinger equation on . Such functions, when in , are known to concentrate a f…
Two-phase free boundary problems in convex domains
Thomas Beck, David Jerison, Sarah Raynor
We study the regularity of minimizers of a two-phase free boundary problem. For a class of n-dimensional convex domains, we establish the Lipschitz continuity of the minimizer up t…
Existence and Stability Properties of Radial Bound States for Schrödinger-Poisson with an External Coulomb Potential in Three Space Dimensions
Sarah Raynor, Jeremy L. Marzuola, Gideon Simpson
We consider radial solutions to the Schrödinger-Poisson system in three dimensions with an external smooth potential with Coulomb-like decay. Such a system can be viewed as a mode…
Asymptotic Stability for KdV Solitons in Weighted Spaces
Brian Pigott, Sarah Raynor
In this work, we consider the stability of solitons for the KdV equation below the energy space, using spatially-exponentially-weighted norms. Using a combination of the -method…