110 citations · 484 across the 51 of their papers we have counts for
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The Zakharov system in 4D radial energy space below the ground state
Zihua Guo, Kenji Nakanishi
We prove dynamical dichotomy into scattering and blow-up (in a weak sense) for all radial solutions of the Zakharov system in the energy space of four spatial dimensions that have…
On scattering for the defocusing quintic nonlinear Schrödinger equation on the two-dimensional cylinder
Xing Cheng, Zihua Guo, Zehua Zhao
In this article, we prove the scattering for the quintic defocusing nonlinear Schrödinger equation on cylinder in . We establish an abstract lin…
On the boundary Strichartz estimates for wave and Schrödinger equations
Zihua Guo, Ji Li, Kenji Nakanishi +1
We consider the estimates for the solutions to the wave and Schrödinger equations in high dimensions. For the homogeneous estimates, we show estimate…
Ill-posedness of the Camassa-Holm and related equations in the critical space
Zihua Guo, Xingxing Liu, Luc Molinet +1
We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa-Holm equation, Degasperis-Procesi equation and Novikov equation etc…
Stability of peakons for the generalized modified Camassa-Holm equation
Zihua Guo, Xiaochuan Liu, Xingxing Liu +1
In this paper, we study orbital stability of peakons for the generalized modified Camassa-Holm (gmCH) equation, which is a natural higher-order generalization of the modified Camas…
Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrödinger equation in the critical frequency case
Zihua Guo, Cui Ning, Yifei Wu
We study the stability theory of solitary wave solutions for the generalized derivative nonlinear Schrödinger equation $$ i\partial_{t}u+\partial_{x}^{2}u+i|u|^{2σ}\partial_x u=0.…