102 research outputs found
Global weak solutions for some Oldroyd models
We investigate an evolutive system of non-linear partial differential
equations derived from Oldroyd models on Non-Newtonian flows. We prove global
existence of weak solutions, in the case of a smooth bounded domain, for
general initial data. The results hold true for the periodic case.Comment: Submitte
Double logarithmic inequality with a sharp constant in four space dimensions
We prove a Log Log inequality with a sharp constant in four dimensions for
radially symmetric functions. We also show that the constant in the Log
estimate is almost sharp
On the lack of compactness in the 2D critical Sobolev embedding
This paper is devoted to the description of the lack of compactness of
in the Orlicz space. Our result is expressed in terms of the
concentration-type examples derived by P. -L. Lions. The approach that we adopt
to establish this characterization is completely different from the methods
used in the study of the lack of compactness of Sobolev embedding in Lebesgue
spaces and take into account the variational aspect of Orlicz spaces. We also
investigate the feature of the solutions of non linear wave equation with
exponential growth, where the Orlicz norm plays a decisive role.Comment: 38 page
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