10 citations · 17 across the 9 of their papers we have counts for
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Generation of vortices in the Ginzburg-Landau heat flow
Michał Kowalczyk, Xavier Lamy
We consider the Ginzburg-Landau heat flow on the two-dimensional flat torus, starting from an initial data with a finite number of nondegenerate zeros -- but possibly very high ini…
Stability of the vortex in micromagnetics and related models
Xavier Lamy, Elio Marconi
We consider line-energy models of Ginzburg-Landau type in a two-dimensional simply-connected bounded domain. Configurations of vanishing energy have been characterized by Jabin, Ot…
On a generalized Aviles-Giga functional: compactness, zero-energy states, regularity estimates and energy bounds
Xavier Lamy, Andrew Lorent, Guanying Peng
Given any strictly convex norm on that is in , we study the generalized Aviles-Giga functional \[I_ε(m):=\int_Ω \left(ε…
Generalized Characteristics for Finite Entropy Solutions of Burgers' Equation
Andres A. Contreras Hip, Xavier Lamy, Elio Marconi
We prove the existence of generalized characteristics for weak, not necessarily entropic, solutions of Burgers' equation \[ \partial_t u +\partial_x \frac{u^2}{2} =0, \] whose entr…
On the stability of radial solutions to an anisotropic Ginzburg-Landau equation
Xavier Lamy, Andrés Zúñiga
We study the linear stability of entire radial solutions , with positive increasing profile , to the anisotropic Ginzburg-Landau equation \[ -Δu -δ(\pa…
On the stability of shock waves for finite-entropy solutions of Burgers
Andres A. Contreras Hip, Xavier Lamy
We prove stability estimates for entropic shocks among weak, possibly \emph{non-entropic}, solutions of scalar conservation laws with strictl…