An improved bilinear estimate for Benjamin-Ono type equations

Details An improved bilinear estimate for Benjamin-Ono type equations An improved bilinear estimate for Benjamin-Ono type equations

2005-09-09

arxiv.org/abs/math/0509218v1

Extended version published as: Well-posedness for equations of Benjamin-Ono type. Illinois J. Math. (2007), Vol. 51, No. 3, pp

Mathematics

Analysis of PDEs

Scientific paper

A bilinear estimate in Fourier restriction norm spaces with applications to
the Cauchy problem associated to u_t - |D|^{\alpha}u_x + uu_x =0 is proved, for
1< \alpha <2. As a consequence, local well-posedness in H^s(\R) \cap
\dot{H}^{-\omega}(\R) follows for s >-{3/4}(\alpha-1) and \omega=1/\alpha-1/2.
This extends to global well-posedness for all s \geq 0.

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