12 citations · 15 across the 12 of their papers we have counts for
4 papers · 2 filters
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…