相关论文: Some remarks on the radius of spatial analyticity …
About thirty years ago we looked for "minimal assumptions" on the data which guarantee that solutions to the $\,2-D\,$ evolution Euler equations in a bounded domain are classical. Classical means here that all the derivatives appearing in…
Based on some elementary estimates for the space-time derivatives of the heat kernel, we use a bootstrapping approach to establish the optimal decay rates for the $L^q(\mathbb{R}^d)$ ($1\leq q\leq\infty$, $d\in\mathbb{N}$) norm of the…
We study spatial analyticity properties of solutions of the Navier-Stokes equations and obtain new growth rate estimates for the analyticity radius. We also study stability properties of strong global solutions of the Navier-Stokes…
In this note, we give the affirmative answer of the question in [18], which is a compactness result of the non-radial Sobolev spaces. As an application, we show the existence of an extremal function of the critical Hardy inequality under…
We consider the Euler equations in a three-dimensional Gevrey-class bounded domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of the solution, up to the boundary, with an explicit estimate on the rate of decay of…
Given strong uniqueness for an It\^o's stochastic equation, we prove that its solution can beconstructed on "any" probability space by using, for example, Euler's polygonal approximations. Stochastic equations in $\mathbb{R}^{d}$ and in…
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of…
We develop a framework for studying quasi-periodic maps and diffeomorphisms on $\mathbb{R}^n$. As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on $\mathbb{R}^n$. In…
We consider the 3D Navier-Stokes equations in the upper half space $\mathbb H^3_+$ with periodic boundary conditions in the horizontal directions. We prove the inviscid limit holds in the topology $L^\infty([0, T]; L^2(\mathbb H^3_+))$…
In this paper, we consider the wave equation in 3-dimensional space with an energy-subcritical nonlinearity, either in the focusing or defocusing case. We show that any radial solution of the equation which is bounded in the critical…
In this paper we shall consider the Navier-Stokes equations in the half plane with Euler-type initial conditions, i.e. initial conditions which have a non-zero tangential component at the boundary. Under analyticity assumptions for the…
We prove the time analyticity for weak solutions of inhomogeneous parabolic equations with measurable coefficients in the half space with either the Dirichlet boundary condition or the conormal boundary condition under the assumption that…
This paper is devoted to the spatial analyticity of the solution of the BBM equation on the real line with an analytic initial data. It is shown that the analytic radius has a lower bound like $t^{-\frac{2}{3}}$ as time $t$ goes to…
We prove a characterization of Hardy's inequality in Sobolev-Slobodecki\u{\i} spaces in terms of positive local weak supersolutions of the relevant Euler-Lagrange equation. This extends previous results by Ancona and Kinnunen & Korte for…
We address the Mach limit problem for the Euler equations in the analytic spaces. We prove that, given analytic data, the solutions to the compressible Euler equations are uniformly bounded in a suitable analytic norm and then show that the…
Let $T$ be a bounded linear operator on a complex Hilbert space $\mathscr{H}.$ We obtain various lower and upper bounds for the numerical radius of $T$ by developing the Euclidean operator radius bounds of a pair of operators, which are…
We establish the validity of the Euler$+$Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only…
Tight lower and upper bounds for the radius of univalence of some normalized Bessel, Struve and Lommel functions of the first kind are obtained via Euler-Rayleigh inequalities. It is shown also that the radius of univalence of the Struve…
For the compressible Euler equations, even when the initial data are uniformly away from vacuum, solution can approach vacuum in infinite time. Achieving sharp lower bounds of density is crucial in the study of Euler equations. In this…
The purpose of this paper is to study radial solutions for steady hydrodynamic model of semiconductors represented by Euler-Poisson equations with sonic boundary. The existence and uniqueness of radial subsonic solution, and the existence…