Zihua Guo

activity

20242026

collaborators

5 papers

math.AP2026

On the well-posedness of the KP-I equation

Zihua Guo, Luc Molinet

We revisit the local well-posedness for the KP-I equation. We obtain unconditional local well-posedness in $H^{s, 0} (R^{2})$ for $s > 3/4$ and unconditional global well-posedn…

math.AP2025

Global solutions to 3D quadratic nonlinear SchrÃ¶dinger-type equation

Zihua Guo, Naijia Liu, Liang Song

We consider the Cauchy problem to the 3D fractional SchrÃ¶dinger equation with quadratic interaction of $u u ˉ$ type. We prove the global existence of solutions and scattering pr…

math.AP2025

Scattering for the Klein-Gordon-Zakharov system in two dimensions

Shijie Dong, Zihua Guo, Kuijie Li

We study the Klein-Gordon-Zakharov system in two spatial dimensions, an important model in plasma physics. For small, smooth, and spatially localized initial data, we establish the…

math.AP2025

Complex-valued solutions of the mKdV equations in generalized Fourier-Lebesgue spaces

Zijun Chen, Zihua Guo, Chunyan Huang

We study the \emph{complex-valued} solutions to the Cauchy problem of the modified Korteweg-de Vries equation on the real line. To study the low-regularity problems, we employ a ge…

math.AP2024

Remark on the low regularity well-posedness of the KP-I equation

Zihua Guo

We study the Cauchy problem to the KP-I equation posed on $R^{2}$ . We prove that it is $C^{0}$ locally well-posed in $H^{s, 0} (R \times R)$ for $s > 1/2$ , which improves the previous re…