325 research outputs found
Global existence for the 2D incompressible isotropic elastodynamics for small initial data
We establish the global existence and the asymptotic behavior for the 2D
incompressible isotropic elastodynamics for sufficiently small, smooth initial
data in the Eulerian coordinates formulation.The main tools used to derive the
main results are, on the one hand, a modified energy method to derive the
energy estimate and on the other hand, a Fourier transform method with a
suitable choice of norm to derive the sharp estimate. We
mention that the global existence of the same system but in the Lagrangian
coordinates formulation was recently obtained by Lei. Our goal is to improve
the understanding of the behavior of solutions. Also we present a different
approach to study nonlinear wave equations from the point of view in
frequency space.Comment: final version for publicatio
Global regularity for the energy-critical NLS on
We establish global existence for the energy-critical nonlinear Schr\"odinger
equation on . This follows similar lines to the work on
but requires new extinction results for linear solutions and
bounds on the first nonlinear iterate at a Euclidean profile that are adapted
to the new geometry.Comment: to appear in the Annales IHP, Analyse non lineaire. arXiv admin note:
text overlap with arXiv:1102.5771, arXiv:1101.452
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