Hs-global well-posedness for semilinear wave equations
نویسندگان
چکیده
منابع مشابه
H-global well-posedness for semilinear wave equations
We consider the Cauchy problem for semilinear wave equations in Rn with n 3. Making use of Bourgain’s method in conjunction with the endpoint Strichartz estimates of Keel and Tao, we establish the Hs-global well-posedness with s < 1 of the Cauchy problem for the semilinear wave equation. In doing so a number of nonlinear a priori estimates is established in the framework of Besov spaces. Our me...
متن کاملIll-Posedness for Semilinear Wave Equations with Very Low Regularity
In this paper, we study the ill-posdness of the Cauchy problem for semilinear wave equation with very low regularity, where the nonlinear term depends on u and ∂tu. We prove a ill-posedness result for the “defocusing” case, and give an alternative proof for the supercritical “focusing” case, which improves the result in [4].
متن کاملGlobal Attractors for Damped Semilinear Wave Equations
The existence of a global attractor in the natural energy space is proved for the semilinear wave equation utt + βut − ∆u + f(u) = 0 on a bounded domain Ω ⊂ R with Dirichlet boundary conditions. The nonlinear term f is supposed to satisfy an exponential growth condition for n = 2, and for n ≥ 3 the growth condition |f(u)| ≤ c0(|u|γ + 1), where 1 ≤ γ ≤ n n−2 . No Lipschitz condition on f is assu...
متن کاملWell Posedness and Control of Semilinear Wave Equations with Iterated Logarithms
Motivated by a classical work of Erdős we give rather precise necessary and sufficient growth conditions on the nonlinearity in a semilinear wave equation in order to have global existence for all initial data. Then we improve some former exact controllability theorems of Imanuvilov and Zuazua. Résumé. Motivé par un travail classique d’Erdős on donne des conditions nécessaires et suffisantes de...
متن کاملOn the Global Well-posedness for the Axisymmetric Euler Equations
This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in critical Besov spaces B 1+3/p p,1 . In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2003
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(03)00305-6