相关论文: Weak dispersion for the Dirac equation on asymptot…

In this paper we prove Strichartz estimates for the Dirac equation on asymptotically flat manifolds. The proof combines the weak dispersive estimates proved by the first two authors with the Strichartz and smoothing estimates for the wave…

We prove local in time Strichartz estimates for the Dirac equation on spherically symmetric manifolds. As an application, we give a result of local well-posedness for some nonlinear models.

In this paper we study global-in-time, weighted Strichartz estimates for the Dirac equation on warped product spaces in dimension $n\geq3$. In particular, we prove estimates for the dynamics restricted to eigenspaces of the Dirac operator…

This paper is concerned with the study of the wave equation on compact surfaces and locally distributed damping. We study the case where the damping is effective in a well-chosen subset of arbitrarily small measure.

We prove local smoothing and weighted Strichartz estimates for the Dirac equation with a Aharonov-Bohm potential. The proof relies on an explicit representation of the solution built in terms of spectral projections.

By studying the warped(or weighted) area-minimizing hypersurface, we prove that the metric can be locally split as a warped product metric under the spectral Ricci or spectral scalar curvature lower bound condition.

We develop analytical methods for nonlinear Dirac equations. Examples of such equations include Dirac-harmonic maps with curvature term and the equations describing the generalized Weierstrass representation of surfaces in three-manifolds.…

In this paper we study warped-product metrics on manifolds of the form $X \setminus Y$, where $X$ denotes either $\mathbb{H}^n$ or $\mathbb{C} \mathbb{H}^n$, and $Y$ is a totally geodesic submanifold with arbitrary codimension. The main…

We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…

We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold $M^n$ admitting real Killing spinors (resp. parallel spinors), there…

Recent work [J.S. Lundeen et al. Nature, 474, 188 (2011)] directly measured the wavefunction by weakly measuring a variable followed by a normal (i.e. `strong') measurement of the complementary variable. We generalize this method to mixed…

We establish a weighted positive mass theorem which unifies and generalizes results of Baldauf--Ozuch and Chu--Zhu. Our result is in fact equivalent to the usual positive mass theorem, and can be regarded as a positive mass theorem for…

We prove some isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We then relate them to inequalities involving the higher order mean-curvature integrals. We also apply our…

We analyze the dispersive properties of a Dirac system perturbed with a magnetic field. We prove a general virial identity; as applications, we obtain smoothing and endpoint Strichartz estimates which are optimal from the decay point of…

We prove a general dispersive estimate for a Schroedinger type equation on a product manifold, under the assumption that the equation restricted to each factor satisfies suitable dispersive estimates. Among the applications are the…

We prove dispersive decay estimates for the one-dimensional Dirac operator and use them to prove asymptotic stability of small gap solitons in the nonlinear Dirac equations with quintic and higher-order nonlinear terms.

The purpose of this paper is to investigate several issues concerning the Dirac equation from a time-frequency analysis perspective. More precisely, we provide estimates in weighted modulation and Wiener amalgam spaces for the solutions of…

This paper aims to show that the Dirac equation coupled to an arbitrary inhomogeneous flux field admits separation in manifolds formed from the direct product of bidimensional spaces. As a direct application of these results, we study a…

The aim of this paper is to understand the influence of a dissipative term which is small in the sense that it is asymptotically below scaling on the asymptotic properties of solutions. A diagonalization procedure is applied in order to…

Exponential decay estimates of a general linear weakly damped wave equation are studied with decay rate lying in a range. Based on the $C^0$-conforming finite element method to discretize spatial variables keeping temporal variable…