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arXiv · 1709.10224

Stabilization of Dispersion Generalized Benjamin Ono

Cynthia Flores·Seungly Oh·Derek Smith
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Abstract

In this article, we examine $L^2$ well-posedness and stabilization property of the dispersion-generalized Benjamin-Ono equation with periodic boundary conditions. The main ingredient of our proof is a development of dissipation-normalized Bourgain space, which gains smoothing properties simultaneously from dissipation and dispersion within the equation. We will establish a bilinear estimate for the derivative nonlinearity using this space and prove the linear observability inequality leading to small-data stabilization.

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Cynthia Flores, Seungly Oh, Derek Smith. 2017-09-29. Stabilization of Dispersion Generalized Benjamin Ono. https://arxiv.org/abs/1709.10224

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