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math.AP2019
On Morawetz estimates with time-dependent weights for the Klein-Gordon equation
Jungkwon Kim, Hyeongjin Lee, Ihyeok Seo +1
We obtain some new Morawetz estimates for the Klein-Gordon flow of the form \begin{equation*} \big\||\nabla|^σ e^{it \sqrt{1-Δ}}f \big\|_{L^2_{x,t}(|(x,t)|^{-α})} \lesssim \|f\|_{H…
math.AP2019
Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential
Hyeongjin Lee, Ihyeok Seo, Jihyeon Seok
We prove weighted estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Ca…