Blow up for the Semilinear Wave Equation in Schwarzschild Metric
نویسندگان
چکیده
We study the semilinear wave equation in Schwarzschild metric (3 + 1 dimensional space time). First, we establish that the problem is locally well posed in H for any σ > 1; then we prove the blow up of the solution for every p > 1 and non negative initial data. The work is dedicated to prof. Yvonne Choquet Bruhat in occasion of her 80th year.
منابع مشابه
Slow Blow up Solutions for Certain Critical Wave Equations
We describe in this article two recent results [11], [12], obtained by the author jointly with W. Schlag and D. Tataru, about singular solutions for the critical wave maps equation, as well as the critical focussing semilinear wave equation. Specifically, the first result [11] establishes for the first time the conjectured formation of singularities for co-rotational wave maps into the sphere S...
متن کاملExistence and classification of characteristic points at blow-up for a semilinear wave equation
We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u(x, t), the graph x 7→ T (x) of its blow-up points and S ⊂ R the set of all characteristic points and show that S has an empty interior. Finally, given x0 ∈ S, we show that in self...
متن کاملExistence and characterization of characteristic points for a semilinear wave equation in one space dimension
Abstract: We consider the semilinear wave equation with power nonlinearity in one space dimension. We first show the existence of a blow-up solution with a characteristic point. Then, we consider an arbitrary blow-up solution u(x, t), the graph x 7→ T (x) of its blow-up points and S ⊂ the set of all characteristic points, and show that the S has an empty interior. Finally, given x0 ∈ S, we show...
متن کاملar X iv : g r - qc / 0 31 00 91 v 2 1 4 A ug 2 00 6 Semilinear wave equations on the Schwarzschild manifold I : Local Decay Estimates
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 inequalities.
متن کاملar X iv : g r - qc / 0 31 00 91 v 1 1 9 O ct 2 00 3 Semilinear wave equations on the Schwarzschild manifold I : Local Decay Estimates
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 inequalities.
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 2004