11 papers
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…
On the Hardy-Hénon heat equation with an inverse square potential
Divyang G. Bhimani, Saikatul Haque, Masahiro Ikeda
We study Cauchy problem for the Hardy-Hénon parabolic equation with an inverse square potential, namely, \[\partial_tu -Îu+a|x|^{-2} u= |x|^γ F_α(u),\] where $a\ge-(\frac{d-2}{…
Pointwise convergence to initial data of heat and Hermite-heat equations in Modulation Spaces
Divyang G. Bhimani, Rupak K. Dalai
We characterize weighted modulation spaces (data space) for which the heat semigroup converges pointwise to the initial data as time tends to zero. Here stan…
On 1D mass subcritical nonlinear Schr\''odinger and Hartree equations in modulation spaces
Divyang G. Bhimani, Diksha Dhingra, Vijay Kumar Sohani
We establish well-posedness theory for the 1D mass-subcritical nonlinear Schrödinger equation (NLS) having power-type nonlinearity in a certain modulation spaces $M^…
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…
Orthonormal Strichartz estimates on torus and waveguide manifold and applications
Divyang G. Bhimani, Subhash. R. Choudhary
We establish new orthonormal Strichartz estimates for the fractional Schrödinger equations on torus and waveguide manifold . We generali…