Related papers: Some Remarks on Strichartz Estimates for Homogeneo…

In this contribution, we provide convergence rates for a finite volume scheme of a stochastic non-linear parabolic equation with multiplicative Lipschitz noise and homogeneous Neumann boundary conditions. More precisely, we give an error…

We prove existence and uniqueness of $L^2$ solutions to the inhomogeneous wave equation on $\mathbb{R}^{n-1}\times\mathbb{R}$ under the assumption that the inhomogeneous data lies in $L^p(\mathbb{R}^n)$ for $p=2n/(n+4)$. We also require the…

We show global-in-time Strichartz estimates for the isotropic Maxwell system with divergence free data. On the scalar permittivity and permeability we impose decay assumptions as $|x|\to\infty$ and a non-trapping condition. The proof is…

We prove better Strichartz type estimates than expected from the (optimal) dispersion we obtained in our earlier work on a 2d convex model. This follows from taking full advantage of the space-time localization of caustics in the parametrix…

We prove dispersive estimates for solutions to the wave equation with a real-valued potential $V\in L^\infty({\bf R}^n)$, $n\ge 4$, satisfying $V(x)=O(|x|^{-(n+1)/2-\epsilon})$, $|x|>1$, $\epsilon>0$.

Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales…

The objective of this paper is to report on recent progress on Strichartz estimates for the Schr\"odinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in…

In this note we study the eigenvalue problem for a quadratic form associated with Strichartz estimates for the Schr\"{o}dinger equation, proving in particular a sharp Strichartz inequality for the case of odd initial data. We also describe…

The paper concerns the sharp boundary regularity estimates in homogenization of Dirichlet problem for Stokes systems. We obtain the Lipschitz estimates for velocity term and $L^\infty$ estimate for pressure term, under some reasonable…

We study local-in-time and global-in-time bilinear Strichartz estimates for the Schr\"odinger equation on waveguides. As applications, we apply those estimates to study global well-posedness of nonlinear Schr\"odinger equations on these…

Let $\Delta_\kappa$ be the Dunkl-Laplacian on $\mathbb{R}^n$. The main aim of this paper is to investigate the orthonormal Strichartz estimates for the Schr\"odinger equation with initial data from the homogeneous Dunkl-Sobolev space…

We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by…

We establish inhomogeneous Strichartz Estimates for the Schr{\"o}dinger equation with singular and time dependent potentials for non-admissible pairs. Our work extends the results provided by Vilela [23] and Foschi [6] where they proved the…

We study rates of convergence of solutions in L^2 and H^{1/2} for a family of elliptic systems {L_\epsilon} with rapidly oscillating oscillating coefficients in Lipschitz domains with Dirichlet or Neumann boundary conditions. As a…

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck…

For any subcritical index of regularity $s>3/2$, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space…

We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order to do this, we also obtain log-scale lossless Strichartz and…

We compute explicitely the best constants and, by solving some functional equations, we find all maximizers for homogeneous Strichartz estimates for the Schrodinger equation and for the wave equation in the cases when the Lebesgue exponent…

We consider the wave equation on a manifold $(\Omega,g)$ of dimension $d\geq 2$ with smooth strictly convex boundary $\partial\Omega\neq\emptyset$, with Dirichlet boundary conditions. We construct a sharp local in time parametrix and then…

This paper is devoted to the study of the inhomogeneous wave equation with singular (less than continuous) time dependent coefficients. Particular attention is given to the role of the lower order terms and suitable Levi conditions are…