12 citations · 15 across the 12 of their papers we have counts for
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Counterexamples to Schiffer's Conjecture
Gonzalo Cao-Labora, Jaume de Dios Pont
The Schiffer conjecture states that if a smooth domain admits a Neumann eigenfunction of the Laplacian which is constant at the boundary, then the domain is…
Instability of two-dimensional Taylor-Green Vortices
Gonzalo Cao-Labora, Maria Colombo, Michele Dolce +1
For a wide class of linear Hamiltonian operators we develop a general criterion that characterizes the unstable eigenvalues as the zeros of a holomorphic function given by the dete…
A contractible Schiffer counterexample on the half-sphere
Gonzalo Cao-Labora, Antonio J. Fernández
We show the existence of a family of nontrivial smooth contractible domains on the sphere that admit Neumann eigenfunctions of the Laplacian which are constant on the boundary. The…
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…
Low regularity analysis of the Zakharov--Kuznetsov equation on
Gonzalo Cao-Labora
We consider the Cauchy problem for the Zakharov-Kuznetsov equation in the cylinder. We improve the local wellposedness to spaces of regularity . The result is optimal in t…
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…
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,…