Low-regularity Global Solutions to Nonlinear Dispersive Equations
نویسنده
چکیده
In these notes we discuss some recent developments in the study of global solutions to dispersive equations, especially for low regularity data.
منابع مشابه
Rough solutions for the periodic Korteweg–de Vries equation
We show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensional Korteweg– de Vries (KdV) equation on a periodic domain and with initial condition in FLα,p spaces. We discuss convergence of Galerkin approximations, a modified Euler scheme and the presence of a random force of w...
متن کاملRegularity of Ground State Solutions of Dispersion Managed Nonlinear Schrödinger Equations
Abstract. We consider the Dispersion Managed Nonlinear Schrödinger Equation in the case of zero residual dispersion. Using dispersive properties of the equation and estimates in Bourgain spaces we show that the ground state solutions of DMNLS are smooth. The existence of smooth solutions in this case matches the well-known smoothness of the solutions in the case of nonzero residual dispersion. ...
متن کاملGlobal regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations
We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori estimates for the growth of spatial gradients. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 35Q30, 82C31, 76A05.
متن کاملGevrey regularity for a class of water-wave models
MSC: 35Q53 35A07 Keywords: Local well posedness Dispersive smoothing Real-analytic solutions Higher-order water-wave models a b s t r a c t Local well posedness for a class of higher-order nonlinear dispersive partial differential equations is obtained in spaces of functions analytic on a strip around the real axis. The proof relies on estimates in space–time norms adapted to the linear part of...
متن کاملAsymptotic behavior of solutions to a class of fourth-order nonlinear evolution equations with dispersive and dissipative terms
We study the long time asymptotic behavior of solutions to a class of fourth-order nonlinear evolution equations with dispersive and dissipative terms. By using the integral estimation method combined with the Gronwall inequality, we point out that the global strong solutions of the problems decay to zero exponentially with the passage of time to infinity. The proof is rigorous and only based o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001