The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited

By Luc Molinet, Didier Pilod. 2010

124 citations recorded by the source corpus.

In a recent work, Ionescu and Kenig proved that the Cauchy problem associatedto the Benjamin-Ono equation is well-posed in $L^2(\mathbb R)$. In this paper we give a simpler proof of Ionescu and Kenig's result, which moreover provides stronger uniqueness results. In particular, we prove unconditional well-posedness in $H^s(\mathbb R)$, for $s>1/4$.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/19ec3bf56037debf1aab07cbd4b69ae7c22f926a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Germán E. Fonseca
2. Gustavo Ponce

In Mathematical Physics

1. Germán E. Fonseca
2. Gustavo Ponce
3. A. Alexandrou Himonas
4. Carlos E. Kenig
5. Fabian Hornung

In Statistical and Nonlinear Physics

1. Germán E. Fonseca
2. Gustavo Ponce
3. A. Alexandrou Himonas
4. Carlos E. Kenig
5. Lorenzo Brandolese

Citations in the corpus

• The IVP for the Benjamin-Ono equation in weighted Sobolev spaces (2010, background): “n [19] (see also [17]) implies that no well-posedness result in Hs(R), s ∈ R can be established by a solely contraction principle arguments. For further results on uniqueness and comments we refer to [18]. Our study here includes both the regularity and the decay of the solution measured in the L2 s”