Related papers: Some remarks on the radius of spatial analyticity …
The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…
In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exact concept of dimension on graphs, classical methods that…
We consider the Cauchy problem for an equation of Korteweg-de Vries-Kawahara type with initial data in the analytic Gevrey spaces. By using linear, bilinear and trilinear estimates in analytic Bourgain spaces, we establish the local…
In 1981, Foias, Guillop\'e and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier-Stokes equation. Such bounds are instructive in the numerical investigation of intermittency often observed in…
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all…
We consider the inhomogeneous heat equation on the half-space $\mathbb R_{+}^{d}$ with Neumann boundary conditions. We prove a space-time Gevrey regularity of the solution, with a radius of analyticity uniform up to the boundary of the…
In this paper we study Strichartz estimates for dispersive equations which are defined by radially symmetric pseudo-differential operators, and of which initial data belongs to spaces of Sobolev type defined in spherical coordinates. We…
We study Toeplitz operators with separately radial and radial symbols on the weighted Bergman spaces on the unit ball. The unitary equivalence of such operators with multiplication operators on $\ell^2$ spaces was previously obtained by…
We consider the three-dimensional incompressible Euler equations in Sobolev conormal spaces and establish local-in-time existence and uniqueness in the half-space or channel. The initial data is Lipschitz having four square-integrable…
We consider the Euler-Korteweg system with space periodic boundary conditions $ x \in \mathbb T^d $. We prove a local in time existence result of classical solutions for irrotational velocity fields requiring natural minimal regularity…
We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with time-independent coefficients and apply them to obtain observability inequalities for its solutions over measurable sets.
In this paper, we study the persistence of spatial analyticity for the solutions to the Klein-Gordon-Schr\"{o}dinger system, which describes a physical system of a nucleon field interacting with a neutral meson field, with analytic initial…
In this work we consider a finite dimensional approximation for the 2D Euler equations on the sphere, proposed by V. Zeitlin, and show their convergence towards a solution to Euler equations with marginals distributed as the enstrophy…
We prove that the time of classical existence of smooth solutions to the relativistic Euler equations can be bounded from below in terms of norms that measure the "(sound) wave-part" of the data in Sobolev space and "transport-part" in…
We introduce a new method for constructing local-in-time solutions the incompressible Euler equations in Sobolev spaces on an arbitrary Sobolev bounded domain. The method is based on construction of an analytic solution in an analytically…
In this paper we present a new characterization of Sobolev spaces on Euclidian spaces ($\mathbb{R}^n$). Our characterizing condition is obtained via a quadratic multiscale expression which exploits the particular symmetry properties of…
We study the inviscid limit of the free boundary Navier-Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a…
A theory of Sobolev inequalities in arbitrary open sets of Euclidean space is established. Boundary regularity of domains is replaced with information on boundary traces of trial functions and of their derivatives up to some explicit…
Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition $\psi_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $\delta(t)$ of its analyticity strip follows a…
In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature.…