Well-posedness for the generalized Benjamin-Ono equations with arbitrary large initial data in the critical space

2008/07/14 by Vento, Stéphane · 1 citation
#35B30 #35Q55 #76B03 #76B55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0807.2193

Abstract

We prove that the generalized Benjamin-Ono equations ∂_tu+H∂_x²u± u^k∂_xu=0, k≥ 4 are locally well-posed in the scaling invariant spaces H^s_k(\R) where s_k=1/2-1/k. Our results also hold in the non-homogeneous spaces H^s_k(\R). In the case k=3, local well-posedness is obtained in H^s(\R), s>1/3.

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