68 citations · 351 across the 40 of their papers we have counts for
43 papers · 1 filter
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…
Homogeneous steady states for the generalized surface quasi-geostrophic equations
Ken Abe, Javier Gómez-Serrano, In-Jee Jeong
We consider homogeneous (stationary self-similar) solutions to the generalized surface quasi-geostrophic (gSQG) equations parametrized by the constant , representing the 2D…
Discovery of Unstable Singularities
Yongji Wang, Mehdi Bennani, James Martens +19
Whether singularities can form in fluids remains a foundational unanswered question in mathematics. This phenomenon occurs when solutions to governing equations, such as the 3D Eul…
A note on the existence of self-similar profiles of the hydrodynamic formulation of the focusing nonlinear Schrödinger equation
Gonzalo Cao-Labora, Javier Gómez-Serrano, Jia Shi +1
After performing the Madelung transformation, the nonlinear Schrödinger equation is transformed into a hydrodynamic equation akin to the compressible Euler equations with a certain…
Existence of analytic non-convex V-states
Gerard Castro-López, Javier Gómez-Serrano
V-states are uniformly rotating vortex patches of the incompressible 2D Euler equation and the only known explicit examples are circles and ellipses. In this paper, we prove the ex…
A note on the periodic Hilbert Transform on a strip
Javier Gómez-Serrano, Sieon Kim
In this note we prove a conjecture by Constantin--Strauss--Vărvărucă related to the finite depth water wave problem, tightening their results. The proof uses identities related to…
Non-radial implosion for the defocusing nonlinear Schrödinger equation in and
Gonzalo Cao-Labora, Javier Gómez-Serrano, Jia Shi +1
In this paper we construct smooth, non-radial solutions of the defocusing nonlinear Schrödinger equation that develop an imploding finite time singularity, both in the periodic set…
Non-radial implosion for compressible Euler and Navier-Stokes in and
Gonzalo Cao-Labora, Javier Gómez-Serrano, Jia Shi +1
In this paper we construct smooth, non-radial solutions of the compressible Euler and Navier-Stokes equation that develop an imploding finite time singularity. Our construction is…
Desingularization of small moving corners for the Muskat equation
Eduardo García-Juárez, Javier Gómez-Serrano, Susanna V. Haziot +1
In this paper, we investigate the dynamics of solutions of the Muskat equation with initial interface consisting of multiple corners allowing for linear growth at infinity. Specifi…
Quasiperiodic solutions of the generalized SQG equation
Javier Gómez-Serrano, Alexandru D. Ionescu, Jaemin Park
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an e…
Smooth self-similar imploding profiles to 3D compressible Euler
Tristan Buckmaster, Gonzalo Cao-Labora, Javier Gómez-Serrano
The aim of this note is to present the recent results in [Buckmaster, Cao-Labora, Gómez-Serrano, arXiv:2208.09445, 2022], concerning the existence of "imploding singularities" for…
Smooth imploding solutions for 3D compressible fluids
Tristan Buckmaster, Gonzalo Cao-Labora, Javier Gómez-Serrano
Building upon the pioneering work [Merle, Raphaël, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022, Invent. Math., 227(1):247-413,…
Self-similar spirals for the generalized surface quasi-geostrophic equations
Claudia García, Javier Gómez-Serrano
In this paper we construct a large class of non-trivial (non-radial) self-similar solutions of the generalized surface quasi-geostrophic equation (gSQG). To the best of our knowled…
Highest Cusped Waves for the Burgers-Hilbert equation
Joel Dahne, Javier Gómez-Serrano
In this paper we prove the existence of a periodic highest, cusped, traveling wave solution for the Burgers-Hilbert equation and give its asymptotic behavi…
Asymptotic self-similar blow-up profile for three-dimensional axisymmetric Euler equations using neural networks
Yongji Wang, Ching-Yao Lai, Javier Gómez-Serrano +1
Whether there exist finite time blow-up solutions for the 2-D Boussinesq and the 3-D Euler equations are of fundamental importance to the field of fluid mechanics. We develop a new…
Existence of non-trivial non-concentrated compactly supported stationary solutions of the 2D Euler equation with finite energy
Javier Gómez-Serrano, Jaemin Park, Jia Shi
In this paper, we prove the existence of locally non-radial solutions to the stationary 2D Euler equations with compact support but non-concentrated around one or several points. O…
Self-similar solutions for the Muskat equation
Eduardo García-Juárez, Javier Gómez-Serrano, Huy Q. Nguyen +1
We show the existence of self-similar solutions for the Muskat equation. These solutions are parameterized by ; they are exact corners of slope at and become s…
Remarks on stationary and uniformly-rotating vortex sheets: Flexibility results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we construct new, uniformly-rotating solutions of the vortex sheet equation bifurcating from circles with constant vorticity amplitude. The proof is accomplished via…
Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results
Javier Gómez-Serrano, Jaemin Park, Jia Shi +1
In this paper, we show that the only solution of the vortex sheet equation, either stationary or uniformly rotating with negative angular velocity , such that it has positive vo…