JournalsaihpcVol. 41, No. 3pp. 725–747

On local energy decay for solutions of the Benjamin–Ono equation

  • Ricardo Freire

    Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

  • Felipe Linares

    Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, Brazil

  • Claudio Muñoz

    Universidad de Chile, Santiago, Chile

  • Gustavo Ponce

    University of California, Santa Barbara, USA
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Abstract

We consider the long time dynamics of large solutions to the Benjamin–Ono equation. Using virial techniques, we describe regions of space where every solution in a suitable Sobolev space must decay to zero along sequences of times. Moreover, in the case of exterior regions, we prove complete decay for any sequence of times. The remaining regions not treated here are essentially the strong dispersion and soliton regions.

Cite this article

Ricardo Freire, Felipe Linares, Claudio Muñoz, Gustavo Ponce, On local energy decay for solutions of the Benjamin–Ono equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 3, pp. 725–747

DOI 10.4171/AIHPC/81