7 papers
Talbot effect for the third order Lugiato-Lefever equation
Gunwoo Cho, Seongyeon Kim, Ihyeok Seo
We discuss the Lugiato-Lefever equation and its variant with third-order dispersion, which are mathematical models used to describe how a light beam forms patterns within an optica…
Remarks on the well-posedness of the energy-critical inhomogeneous Hartree equation
Seongyeon Kim, Tarek Saanouni, Ihyeok Seo
We study the energy-critical inhomogeneous Hartree equation in space dimensions three and higher. Previous local well-posedness results left open the parameter regime where the inh…
Explicit inversion for variable-speed wave equations on bounded domains
Sunghwan Moon, Ihyeok Seo
We study the reconstruction of the initial pressure for the wave model \[ \partial_t^2 p(x,t)=c(x)Î_{x}p(x,t)\qquad (x,t)\inΩ\times[0,\infty), \] posed on a bounded…
On Morawetz estimates for the elastic wave equation
Seongyeon Kim, Ihyeok Seo
We establish Morawetz-type estimates for solutions to the elastic wave equation with singular weights of the form or . In particular, we show that space-…
On the radius of spatial analyticity for the Majda-Biello and Hirota-Satsuma systems
Seongyeon Kim, Ihyeok Seo
We investigate the persistence of spatial analyticity for solutions to the Majda-Biello and Hirota-Satsuma systems with analytic initial data. This result is the first to establish…
On Dirac equations with Hartree type nonlinearity in modulation spaces
Seongyeon Kim, Hyeongjin Lee, Ihyeok Seo
We obtain the local well-posedness for Dirac equations with a Hartree type nonlinearity derived by decoupling the Dirac-Klein-Gordon system. We extend the function space of initial…