J. Gómez-Serrano

activity

20102026

most citedExistence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations

68 citations · 351 across the 40 of their papers we have counts for

collaborators

52 papers

math.FA2026

Contractivity of Rudin's diagonal restriction operator for $H^{p}$ of the polydisc

Ole Fredrik Brevig, Javier Gómez-Serrano, Joaquim Ortega-Cerdà +1

We establish that Rudin's diagonal restriction operator is contractive from the Hardy space $H^{p}$ of the bidisc to the Bergman space $A^{p}$ of the disc for $2 \leq p < \infty$ , and cha…

math.AP2026

Counterexamples to Grad's conjecture

Javier Gómez-Serrano, Lukas Liehr, Mitchell A. Taylor

For each sufficiently large $N$ , we construct smooth solutions of the magnetohydrostatic equations on embedded solid tori whose regular pressure levels are nested tori, whose magne…

math.AP2026

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}…

math.AP2026

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 $L_{0} > 0$ and one smooth, compactly…

math.MG2026

An isoperimetric problem for Fourier zeros of centrally symmetric convex bodies

Javier Gómez-Serrano, Michael Levitin, Daniel Platt +1

Given a centrally symmetric convex body, consider the zero set of the Fourier transform of its characteristic function. We study how large the distance from this set to the origin…

math.RT2026

On The Eaton-Moretó Conjecture for Principal Blocks of Finite Groups

Asier Arranz, Javier Gómez-Serrano, Gabriel Navarro +1

Let $G$ be a finite group and let $p$ be a prime. If $P$ is a nonabelian Sylow $p$ -subgroup of $G$ and $m (P)$ is the smallest non-linear irreducible character degree of $P$ , we pro…

math.AP2026

The energy of fractional Allen--Cahn layers in dimension one

Alvaro Carballeira, Damien Galant, Javier Gómez-Serrano

We study the energy $E (s) := E_{s} [Φ_{s}]$ of the one-dimensional fractional Allen--Cahn layer solution $Φ_{s}$ , defined as the unique odd, increasing solution of $(-Δ)^{s} Φ…

math.AP2026

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 $T$ in the regime of small frequency $ω$ and large wave speed $c$ . For $ω = 3$ and $c…

math.AP2026

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…

math.SP2026

Monotonicity of the first Dirichlet eigenvalue of regular polygons

Joel Dahne, Javier Gómez-Serrano, Joana Pech-Alberich

In this paper we prove that the first Dirichlet eigenvalue $λ_{1}^{N}$ of an $N$ -sided regular polygon of fixed area is a monotonically decreasing function of $N$ for all $N \geq 3$ , a…

cs.NE2025★ 3 cited

Mathematical exploration and discovery at scale

Bogdan Georgiev, Javier Gómez-Serrano, Terence Tao +1

AlphaEvolve (Novikov et al., 2025) is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary f…

math.AP2025

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 $0 < s < 1$ , representing the 2D…

math.AP2025

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…

math.AP2025

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…

math.AP2024

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…

math.AP2024

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…

math.AP2024

Non-radial implosion for the defocusing nonlinear Schrödinger equation in $T^{d}$ and $R^{d}$

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…

math.AP2023

Non-radial implosion for compressible Euler and Navier-Stokes in $T^{3}$ and $R^{3}$

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…

math.AP2023★ 1 cited

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…

math.AP2023

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…

math.AP2023

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…

math.AP2022★ 12 cited

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,…

math.AP2022★ 1 cited

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…

math.AP2022★ 7 cited

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 $f_{t} + f f_{x} = H [f]$ and give its asymptotic behavi…

Contractivity of Rudin's diagonal restriction operator for Hp of the polydisc

Counterexamples to Grad's conjecture

Blow-up for energy supercritical defocusing nonlinear Schrödinger equations in dimensions three, four and five

Double-wells in a strong magnetic field: absence of tunneling for infinitely many values of the coupling constant

An isoperimetric problem for Fourier zeros of centrally symmetric convex bodies

On The Eaton-Moretó Conjecture for Principal Blocks of Finite Groups

The energy of fractional Allen--Cahn layers in dimension one

Linear instability of a Burgers--Hilbert traveling wave

Nested nodal loops of biharmonic functions

Monotonicity of the first Dirichlet eigenvalue of regular polygons

Mathematical exploration and discovery at scale

Homogeneous steady states for the generalized surface quasi-geostrophic equations

Discovery of Unstable Singularities

A note on the existence of self-similar profiles of the hydrodynamic formulation of the focusing nonlinear Schrödinger equation

Existence of analytic non-convex V-states

A note on the periodic Hilbert Transform on a strip

Non-radial implosion for the defocusing nonlinear Schrödinger equation in Td and Rd

Non-radial implosion for compressible Euler and Navier-Stokes in T3 and R3

Desingularization of small moving corners for the Muskat equation

Quasiperiodic solutions of the generalized SQG equation

Smooth self-similar imploding profiles to 3D compressible Euler

Smooth imploding solutions for 3D compressible fluids

Self-similar spirals for the generalized surface quasi-geostrophic equations

Highest Cusped Waves for the Burgers-Hilbert equation

Contractivity of Rudin's diagonal restriction operator for $H^{p}$ of the polydisc

Non-radial implosion for the defocusing nonlinear Schrödinger equation in $T^{d}$ and $R^{d}$

Non-radial implosion for compressible Euler and Navier-Stokes in $T^{3}$ and $R^{3}$