arXiv subjects

Jihyeon Seok

Publications and source records attributed to Jihyeon Seok.

4 recordsLinked to original sources

arXiv2021

On local-in-time Strichartz estimates for the Schrödinger equation with singular potentials

There have been a lot of works concerning the Strichartz estimates for the perturbed Schrödinger equation by potential. These can be basically carried out adopting the well-known procedure for obtaining the Strichartz estimates from the weighted $L^2$ resolvent estimates for the Laplacian. In this paper we handle the Strichartz estimates without relying on the resolvent estimates. This enables us to consider various potential classes such as the Morrey-Campanato classes.

math.AP↗

arXiv2020

On Morawetz estimates with time-dependent weights for the Klein-Gordon equation

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^s} \end{equation*} where $σ,s\geq0$ and $α>0$. The conventional approaches to Morawetz estimates with $|x|^{-α}$ are no longer available in the case of time-dependent weights $|(x,t)|^{-α}$. Here we instead apply the Littlewood-Paley theory with Muckenhoupt $A_2$ weights to frequency localized estimates thereof that are obtained by making use of the bilinear interpolation between their bilinear form estimates which need to carefully analyze some relevant oscillatory integrals according to the different scaling of $\sqrt{1-Δ}$ for low and high frequencies.

math.AP↗

arXiv2019

Note on Strichartz inequalities for the wave equation with potential

We obtain Strichartz inequalities for the wave equation with potentials which behave like the inverse square potential $|x|^{-2}$ but might be not a radially symmetric function.

math.AP↗

arXiv2019

Local smoothing and Strichartz estimates for the Klein-Gordon equation with the inverse-square potential

We prove weighted $L^2$ estimates for the Klein-Gordon equation perturbed with singular potentials such as the inverse-square potential. We then deduce the well-posedness of the Cauchy problem for this equation with small perturbations, and go on to discuss local smoothing and Strichartz estimates which improve previously known ones.

math.AP↗