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On the wave equation with Coulomb potential
Liang Li, Shenghao Luo, Ruipeng Shen
Wave/Schrödinger equations with potentials naturally originates from both the quantum physics and the study of nonlinear equations. The distractive Coulomb potential is a quantum m…
Channel-localized Strichartz estimates of radial wave equations
Liang Li, Shenghao Luo, Ruipeng Shen
In this work we give a few new Strichartz estimates of radial solutions to the wave equation. These Strichartz estimates still use type norms in each channel-like region…
Decay Estimates of High Dimensional Adjoint Radon Transforms
Ruipeng Shen
In this paper we prove an optimal decay estimate of the adjoint Radon transform of compactly supported data in -dimensional space via a geometric method. A similar…
A Semi-linear Energy Critical Wave Equation With Applications
Ruipeng Shen
In this work we consider a semi-linear energy critical wave equation in () \[ \partial_t^2 u - Δu = \pm ϕ(x) |u|^{4/(d-2)} u, \qquad (x,t)\in {\math…
I-method for Defocusing, Energy-Subcritical Non-linear Wave Equation
Ruipeng Shen
In this paper the author considers the global existence and well-posedness of the non-linear wave equation in 3-dimensional space, assuming tha…