From the 1 of 4 linked papers with an AI index.
4 papers
The stochastic Keller--Segel system in critical spaces
Jae-Hwan Choi, Ankit Kumar, Andrea Pitrone +2
The paper analyzes stochastic Keller–Segel equations on a d‑dimensional torus within scaling‑critical Besov spaces, establishing local well‑posedness and showing that, for sufficie…
A regularity theory for an initial value problem with a time-measurable pseudo-differential operator in a weighted -space
Jae-Hwan Choi, Ildoo Kim, Jin Bong Lee
In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differ…
An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity
Jae-Hwan Choi, Ildoo Kim
We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This…
An existence and uniqueness theory to stochastic partial differential equations involving pseudo-differential operators driven by space-time white noise
Jae-Hwan Choi, Ildoo Kim
In this paper, we aim to develop a new weak formulation that ensures well-posedness for a broad range of stochastic partial differential equations with pseudo-differential operator…