Related papers: Randomization improved Strichartz estimates and gl…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…
The purpose of this article is to construct global solutions, in a probabilistic sense, for the nonlinear Schr{\"o}dinger equation posed on $\mathbb{R}^d$, in a supercritical regime. Firstly, we establish Bourgain type bilinear estimates…
In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.
We study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on Damek-Ricci spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain global…
The aim of the paper is twofold. We establish refined Strichartz estimates for the Schr\"odinger equation on tori within the framework of partial regularity. As a result, we reveal that the solution of the free Schr\"odinger equation has…
Accurately estimating the proportion of true signals among a large number of variables is crucial for enhancing the precision and reliability of scientific research. Traditional signal proportion estimators often assume independence among…
We study the propagation of wave packets for nonlinear nonlocal Schrodinger equations in the semi-classical limit. When the kernel is smooth, we construct approximate solutions for the wave functions in subcritical, critical and…
Recently, the Strichartz estimates for the damped wave equation was obtained by the first author except for the wave endpoint case. In the present paper, we give the Strichartz estimate in the wave endpoint case. We slightly modify the…
We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
We establish new Strichartz estimates for orthonormal families of initial data in the case of the wave, Klein-Gordon and fractional Schr\"odinger equations. Our estimates extend those of Frank-Sabin in the case of the wave and Klein-Gordon…
We prove global well-posedness for the half-wave map with $S^2$ target for small $\dot{H}^{\frac{n}{2}} \times \dot{H}^{\frac{n}{2}-1}$ initial data. We also prove the global well-posedness for the equation with $\mathbb{H}^2$ target for…
In this paper, we establish the well-posedness in energy space for the quintic energy critical wave inside a cylindrical convex domain $\Omega\subset\mathbb{R}^3$ with smooth boundary $\partial\Omega\neq\emptyset$. The key tools to prove…
A new method for estimating the relative positions of location-unaware nodes from the location-aware nodes and the received signal strength (RSS) between the nodes, in a wireless sensor network (WSN), is proposed. In the method, a…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
A number of pulsar timing arrays have recently reported preliminary evidence for the existence of a nanohertz frequency gravitational-wave background. These analyses rely on detailed noise analyses, which are inherently complex due to the…
We establish new Carleman estimates for the wave equation, which we then apply to derive novel observability inequalities for a general class of linear wave equations. The main features of these inequalities are that (a) they apply to a…
In this article, we follow the strategies, listed in \cite{Burq2011} and \cite{OhPo}, in dealing with supercritical cubic and quintic wave equations, we obtain that, the equation \begin{equation*} \left\{ \begin{split}…
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…