Related papers: Some sharp bilinear space-time estimates for the w…
The possibility of finite-time, dispersive blow up for nonlinear equations of Schroedinger type is revisited. This mathematical phenomena is one of the possible explanations for oceanic and optical rogue waves. In dimension one, the…
We consider a large class of harmonic systems, each defined as a quasi-free dynamics on the Weyl algebra over $\ell^2(\mathbb{Z}^d)$. In contrast to recently obtained, short-time locality estimates, known as Lieb-Robinson bounds, we prove a…
This paper describes the partial wave expansion and integral representation of Bessel beams in free space and in the presence of dispersion. The expansion of the Bessel beam wavepacket with constant spectrum is obtained as well.…
We investigate whether a fundamental solution of the Schr\"odinger equation $\partial_t u =(\Delta +V)\, u$ has local in time sharp Gaussian estimates. We compare that class with the class of $V$ for which local in time plain Gaussian…
We prove dispersive estimates for the wave and Schrodinger groups associated to a second-order elliptic self-adjoint operator depending on a semi-classical parameter. Applications are made to non-trapping metric perturbations and to…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
The semilinear wave equation on the (outer) Schwarzschild manifold is studied. We prove local decay estimates for general (non-radial) data, deriving a-priori Morawetz type estimates.
Given a Hilbert space, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with discrete non-negative spectrum acting on it. We consider the cases when the time-dependent propagation speed is regular,…
The $X^{s,b}$ spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain…
We study damped wave propagation problems phrased as abstract evolution equations in Hilbert spaces. Under some general assumptions, including a natural compatibility condition for initial values, we establish exponential decay estimates…
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…
We obtain a sharp bilinear restriction estimate for the paraboloid in $\mathbb{R}^3$ for $q>3.25$.
The irreducible representations of the extended Galilean group are used to derive the symmetric and asymmetric wave equations. It is shown that among these equations only a new asymmetric wave equation is fundamental. By being fundamental…
This paper establishes a sharp, expanded wave-breaking criterion for a class of nonlinear nonlocal Whitham-type equations, significantly generalizing the classical threshold introduced by Seliger. While the system of inequalities governing…
We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is…
We consider the scalar wave equation in the Kerr geometry for Cauchy data which is smooth and compactly supported outside the event horizon. We derive an integral representation which expresses the solution as a superposition of solutions…
In this paper we focus on the global-in-time existence and the pointwise estimates of solutions to the initial value problem for the semilinear dissipative wave equation in multi-dimensions. By using the method of Green function combined…
In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analyzing the properties of its fundamental solution, we…
We prove dispersive estimate for the elastic wave equation by which we extend the known Strichartz estimates for the classical wave equation to those for the elastic wave equation. In particular, the endpoint Strichartz estimates are…