Related papers: Strichartz estimates for the Dirac equation on asy…

We illustrate how to compute asymptotic interactions between discrete solitary waves of dispersive equations, using the approach proposed by Manton [Nucl. Phys. B 150, 397 (1979)]. We also discuss the complications arising due to…

We prove sharper Strichartz estimates than expected from theoptimal dispersion bounds.

We study the asymptotic Dirichlet problem for A-harmonic equations and for the minimal graph equation on a Cartan-Hadamard manifold M whose sectional curvatures are bounded from below and above by certain functions depending on the distance…

In this paper we verify the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds when n=3,4, we also give an almost sharp life span for the subcritical case $2\le p<p_c$ when n=3. The main ingredients…

We establish global well-posedness and scattering for the cubic Dirac equation for small data in the critical space $H^1(\mathbb{R}^3)$. The main ingredient is obtaining a sharp end-point Strichartz estimate for the Klein-Gordon equation.…

In this paper, we obtain sharp Strichartz estimates for solutions of the wave equation $\square_\gg\phi=0$ where $\gg$ is a rough Lorentzian metric on a 4 dimensional space-time $\MM$. This is the last step of the proof of the bounded $L^2$…

Let $\Delta_\kappa$ be the Dunkl Laplacian on $\mathbb{R}^n$ and $\phi: \mathbb{R}^+ \to \mathbb{R}$ is a smooth function. The aim of this manuscript is twofold. First, we study the decay estimate for a class of dispersive semigroup of the…

We prove Strichartz estimates without loss for the Schr\"odinger equation and the wave equation outside finitely many strictly convex obstacles verifying Ikawa's condition, extending the approach we introduced previously for the two convex…

Einstein-Dirac equations for two spinor fields are considered. It is shown that in this case one can obtain self-consistent equations set for these gravitating spinors. The key idea to obtain Einstein-Dirac equations is to use special…

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.…

We provide reversed Strichartz estimates for the shifted wave equations on non-trapping asymptotically hyperbolic manifolds using cluster estimates for spectral projectors proved previously in such generality. As a consequence, we solve a…

We prove that equality within the Minkowski inequality for asymptotically flat static manifolds is achieved only by slices of Schwarzschild space.

A priori estimates for the mean curvature evolution of Killing graphs in Cartan-Hadamard manifolds with asymptotic Dirichlet conditions are established. As an application, the existence of the corresponding parabolic flow is proved,…

In this short paper, we prove Strichartz estimates for N-body Schr\"odinger equations in the waveguide manifold setting (i.e. on semiperiodic spaces $\mathbb{R}^m\times \mathbb{T}^n$ where $m\geq 3$), provided that interaction potentials…

We prove global Strichartz estimates without loss for the wave equation outside two strictly convex obstacles, following the roadmap introduced in [Lafontaine, 2017] for the Schr\"odinger equation. Moreover, we show a first step toward the…

We consider the Dirac equation with cubic Hartree-type nonlinearity derived by uncoupling the Dirac-Klein-Gordon systems. We prove small data scattering result in full subcritical range. Main ingredients of the proof are the localized…

We prove almost Strichartz estimates found after adding regularity in the spherical coordinates for Schr\"odinger-like equations. The estimates are sharp up to endpoints. The proof relies on estimates involving spherical averages. Sharpness…

We prove global Strichartz estimates without loss outside two strictly convex obstacles, combining arguments from M.Ikawa (1982,1988) with more recent ones inspired by N.Burq, C.Guillarmou, and A. Hassell (2010) and O. Ivanovici (2010).…

Sharp Strichartz estimates are proved for Schr\"odinger and wave equations with Lipschitz coefficients satisfying additional structural assumptions. We use Phillips functional calculus as a substitute for Fourier inversion, which shows how…

We study linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local energy decay and the scattering theory for these models are…