Robert Jerrard

Professor | University of Toronto, Department of Mathematics

Toronto, ON, CANADA

Professor Jerrad's research focuses on nonlinear partial differential equations

Industry Applications (2)

Education/Learning

Research

Research Interests (2)

Calculus of Variations

Nonlinear Partial Differential Equations

Links (1)

Home Page of Robert L. Jerrard

Articles (5)

On the vortex filament conjecture for Euler flows

arXiv

2016 In this paper, we study the evolution of a vortex filament in an incompressible ideal fluid. Under the assumption that the vorticity is concentrated along a smooth curve in $\ mathbb {R}^ 3$, we prove that the curve evolves to leading order by binormal curvature flow.

Weighted TV minimization and applications to vortex density models

arXiv

2015 Motivated in part by models arising from mathematical descriptions of Bose-Einstein condensation, we consider total variation minimization problems in which the total variation is weighted by a function that may degenerate near the domain boundary, and the fidelity term contains a weight that may be both degenerate and singular. We develop a general theory for a class of such problems, with special attention to the examples arising from physical models.

Accelerating fronts in semilinear wave equations

Rendiconti del Circolo Matematico di Palermo

2015 We study dynamics of interfaces in solutions of the equation ε□u+1εfε(u)=0ε◻u+1εfε(u)=0, for fεfε of the form fε(u)=(u2−1)(2u−εκ)fε(u)=(u2−1)(2u−εκ), for κ∈Rκ∈R, as well as more general, but qualitatively similar, nonlinearities. We prove that for suitable initial data, solutions exhibit interfaces that sweep out timelike hypersurfaces of mean curvature proportional to κκ.

Hydrodynamic limit of the Gross-Pitaevskii equation

Communications in Partial Differential Equations

2015 We study dynamics of vortices in solutions of the Gross-Pitaevskii equation i∂ tu= Δ u+ ϵ− 2 u (1−| u| 2) on ℝ2 with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter ϵ.

On the regularity of timelike extremal surfaces

Communications in Contemporary Mathematics

2015 We study a class of timelike weakly extremal surfaces in flat Minkowski space ℝ1+ n, characterized by the fact that they admit a C1 parametrization (in general not an immersion) of a specific form. We prove that if the distinguished parametrization is of class Ck, then the surface is regularly immersed away from a closed singular set of Euclidean Hausdorff dimension at most 1+ 1/k, and that this bound is sharp.