68 citations · 351 across the 40 of their papers we have counts for
6 papers · 2 filters
Counterexamples to Grad's conjecture
Javier Gómez-Serrano, Lukas Liehr, Mitchell A. Taylor
For each sufficiently large , we construct smooth solutions of the magnetohydrostatic equations on embedded solid tori whose regular pressure levels are nested tori, whose magne…
Blow-up for energy supercritical defocusing nonlinear Schrödinger equations in dimensions three, four and five
Kevin Buck, Alvaro Carballeira, Javier Gómez-Serrano +1
We prove finite time blow-up from smooth, radial, compactly supported initial data for the energy supercritical defocusing nonlinear Schrödinger equation $i\partial_tu+Δu-|u|^{p-1}…
Double-wells in a strong magnetic field: absence of tunneling for infinitely many values of the coupling constant
Kevin Buck, Charles L. Fefferman, Javier Gómez-Serrano +3
We prove the fixed-potential conjecture of Fefferman, Shapiro, and Weinstein for inversion-symmetric magnetic double wells. We construct a number and one smooth, compactly…
The energy of fractional Allen--Cahn layers in dimension one
Alvaro Carballeira, Damien Galant, Javier Gómez-Serrano
We study the energy of the one-dimensional fractional Allen--Cahn layer solution , defined as the unique odd, increasing solution of $(-Δ)^{s} Φ…
Linear instability of a Burgers--Hilbert traveling wave
Ángel Castro, Javier Gómez-Serrano, Miguel M. G. Pascual-Caballo
We study the stability of traveling wave solutions to the Burgers--Hilbert equation on in the regime of small frequency and large wave speed . For and $c…
Nested nodal loops of biharmonic functions
Javier Gómez-Serrano, Robert Koirala, Alexander Logunov
Given any \(n\in\mathbb{N}\), we construct a real-valued biharmonic polynomial on \(\mathbb{R}^2\) whose zero set contains a nest of \(n\) smooth, disjoint topological loops, meani…