16 citations · 23 across the 34 of their papers we have counts for
5 papers · 1 filter
Confinement effects for semilinear fractional Hermite heat equations with nonlinearities of arbitrarily rapid growth
Divyang G. Bhimani, Mohamed Majdoub, Ramesh Manna
We study the Cauchy problem for a semilinear heat equation driven by the fractional harmonic oscillator. We establish local and global well-posedness in Orlicz and Morse--Transue s…
Pointwise convergence for single-particle Schrödinger equation and Schrödinger equation with infinitely many particles on the torus and waveguide manifolds
Divyang G. Bhimani, Subhash R. Choudhary
In 1980, Carleson posed a question about the least regularity required for initial data in a Sobolev space to ensure pointwise convergence of the solution to the single parti…
Inhomogeneous nonlinear Schrödinger equation in Fourier-Lebesgue and modulation spaces
Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani
The purpose of this work is to provide a broader framework for analyzing the inhomogeneous nonlinear Schrödinger equation (INLS) \[iu_t + u_{xx} \pm |x|^{-b}|u|^{α-1}u=0, \quad 1<α…
Fefferman--Stein-type estimates and fractional NLS in Fourier Sobolev spaces
Divyang G. Bhimani, Ryosuke Hyakuna
In this paper, we prove a sharp Fefferman--Stein-type estimate for the fractional Schrödinger equation, which can be regarded as a generalized Strichartz estimate for data in the F…
Refined Strichartz estimates and their orthornomal counterparts for Schrödinger equations on torus
Divyang G. Bhimani, Subhash. R. Choudhary, S. S. Mondal
The aim of the paper is twofold. We establish refined Strichartz estimates for the Schrödinger equation on tori within the framework of partial regularity. As a result, we reveal t…