相关论文: On the radius of analyticity of solutions to semi-…

We analyze the instantaneous growth of analyticity radius for three dimensional generalized Navier-Stokes equations. For the subcritical $H^{\gamma}(\mathbb R^3)$ case with $\gamma>\frac12,$ we prove that there exists a positive time $t_0$…

We study the problem of propagation of analytic regularity for semi-linear symmetric hyperbolic systems. We adopt a global perspective and we prove that if the initial datum extends to a holomorphic function in a strip of radius (=width)…

We address the problem of analyticity up to the boundary of solutions to the Euler equations in the half space. We characterize the rate of decay of the real-analyticity radius of the solution $u(t)$ in terms of $\exp{\int_{0}^{t} \Vert…

Persistence of spatial analyticity is studied for solution of the beam equation $ u_{tt} + \left(m+\Delta^2\right) u + |u|^{p-1}u = 0$ on $\mathbb R^n \times \mathbb R$. In particular, for a class of analytic initial data with a uniform…

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{-1/4}$ as time $t$ goes to infinity. This improves the works [Selberg, da Silva, Lower…

We consider the initial value problem for the Dirac-Klein-Gordon equations in two space dimensions. Global regularity for $C^\infty$ data was proved by Gr\"unrock and Pecher. Here we consider analytic data, proving that if the initial…

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…

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 consider the Euler equations on $\mathbb{T}^d$ with analytic data and prove lower bounds for the radius of spatial analyticity $\epsilon(t)$ of the solution using a new method based on inductive estimates in standard Sobolev spaces. Our…

In this paper, we establish the space-time analyticity of global solutions to the incompressible Navier-Stokes equations with small initial data in critical \emph{Besov} spaces $\dot B^{3/p-1}_{p,q}$. Time decay rates of higher order…

In this paper we obtain lower bounds on the radius of spatial analyticity of solutions to the Kawahara equation $u_t + uu_x + \alpha u_{xxx} + \beta u_{xxxxx} = 0$, $\beta\neq0$, given initial data which is analytic with a fixed radius. It…

We show that the uniform radius of spatial analyticity $\sigma(t)$ of solutions at time $t$ to the fifth order KdV-BBM equation cannot decay faster than $1/ \sqrt{t}$ for large $t$, given initial data that is analytic with fixed radius…

We consider the incompressible Navier-Stokes equations in the cylinder $\R \times \T$, with no exterior forcing, and we investigate the long-time behavior of solutions arising from merely bounded initial data. Although we do not know if…

We address the inviscid limit for the Navier-Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and has finite Sobolev regularity in the complement. We prove that for such data…

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 $L^\infty([0, T]; L^2(\mathbb H^3_+))$…

It is shown that the uniform radius of spatial analyticity $\sigma(t)$ of solutions at time $t$ to the 1d, 2d and 3d cubic nonlinear Schr\"{o}dinger equations cannot decay faster than $1/|t|$ as $|t| \to \infty$, given initial data that is…

It is shown that the uniform radius of spatial analyticity $\sigma(t)$ of solutions at time $t$ to the KdV equation cannot decay faster than $|t|^{-4/3}$ as $|t| \to \infty$ given initial data that is analytic with fixed radius $\sigma_0$.…

This paper is concerned with the cubic Szeg\H{o} equation $$ i\partial_t u=\Pi(|u|^2 u), $$ defined on the $L^2$ Hardy space on the one-dimensional torus $\mathbb T$, where $\Pi: L^2(\mathbb T)\rightarrow L^2_+(\mathbb T)$ is the Szeg\H{o}…

Supposing only that $\displaystyle\lim_{t \to 0} \frac{f(t)}{t} = 0$ and $\displaystyle\lim_{t \to \infty} \frac{f(t)}{t^{p}} = 0$, for some $p \in \left(1,\frac{N+1}{N-1}\right)$, we prove that solutions to the extension problem…