G. Cao-Labora

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math.AP2025

Low regularity analysis of the Zakharov--Kuznetsov equation on $R \times T$

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 $s > 1/2$ . The result is optimal in t…

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…

Low regularity analysis of the Zakharov--Kuznetsov equation on R×T

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

Low regularity analysis of the Zakharov--Kuznetsov equation on $R \times T$

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