32 citations · 70 across the 30 of their papers we have counts for
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The radiation theory of radial solutions to 3D energy critical wave equations
Ruipeng Shen
In this work we consider a wide range of energy critical wave equation in 3-dimensional space with radial data. We are interested in exterior scattering phenomenon, in which the as…
Classification of radial non-radiative solutions to the 5D nonlinear wave equations
Liang Li, Ruipeng Shen, Chenhui Wang
In this work we classify all radial non-radiative solutions to the 5D nonlinear wave equations with a wide range of energy critical nonlinearity. We show that such a solution alway…
Radiation fields and non-radiative solutions to the energy sub-critical wave equations
Liang Li, Ruipeng Shen, Chenhui Wang
Radiation field and channel of energy method have become important tools in the study of nonlinear wave equations in recent years. In this work we give basic theory of radiation fi…
Asymptotic behaviour of non-radiative solution to the wave equations
Liang Li, Ruipeng Shen, Chenhui Wang +1
In this work we consider weakly non-radiative solutions to both linear and non-linear wave equations. We first characterize all weakly non-radiative free waves, without the radial…
An inequality regarding non-radiative linear waves via a geometric method
Liang Li, Ruipeng Shen, Chenhui Wang
In this work we consider the operator \[ (\mathbf{T} G) (x)= \int_{\mathbb{S}^2} G(x\cdot ω, ω) dω, \quad x\in \mathbb{R}^3, \; G\in L^2(\mathbb{R}\times \mathbb{S}^2). \] This is…