281 research outputs found
Asymptotic Behavior of the Einstein-Yang-Mills-Dilaton System for a Closed Friedmann-Lemaitre Universe
We study the coupled Einstein-Yang-Mills-Dilaton (EYMD) equations for a
Fried\-mann-Le\-mai\-tre universe with constant curvature . Our detailed
analysis is restricted to the case where the dilaton potential and the
cosmological constant vanish. Also assuming a static gauge field, we present
analytical and numerical results on the behavior of solutions of the EYMD
equations. For different values of the dilaton coupling constant we analyze the
phase portrait for the time evolution of the dilaton field and give the
behavior of the scale factor. It turns out that there are no inflationary
stages in this model.Comment: 18 pages, Uuencoded gzip compressed tar file containing a latex file
and 12 figures. The epsfig.sty is neede
On the cauchy problem for a coupled system of kdv equations : critical case
We investigate some well-posedness issues for the initial value problem associated to the system
\begin{equation*}
\begin{cases}
u_{t}+\partial_x^3u+\partial_x(u^2v^3) =0,\\
v_{t}+\partial_x^3v+\partial_x(u^3v^2)=0,
\end{cases}
\end{equation*}
for given data in low order Sobolev spaces .
We prove local and global well-posedness results utilizing the sharp smoothing estimates associated to the linear problem combined with the contraction mapping principle. For data with small Sobolev norm we obtain global solution whenever by using global smoothing estimates.
In particular, for data satisfying
,
where is solitary wave solution, we get global solution whenever .
To prove this last result, we apply the splitting argument introduced by Bourgain [5] and further simplified by Fonseca, Linares and Ponce [6, 7].Fundação para a Ciência e a Tecnologia (FCT) - POCI 2010/FEDER, bolsa SFRH/BPD/22018/2005Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP
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