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arXiv · 2503.15480

The Cauchy problem for nonlinear dispersive models of long internal waves in the presence of the Coriolis force

Ricardo Freire·Thyago S. R. Santos
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Abstract

We investigate models of dispersive long internal waves with rotational effects, specifically the Benjamin-Ono (BO) and intermediate long wave (ILW) equations modified by the presence of the nonlocal operator $\partial_x^{-1}$, which mathematically accounts for rotational influences. We establish a local and global well-posedness theory while ensuring the unconditional uniqueness of solutions in low-regularity Sobolev-type spaces. Our approach is based on techniques introduced by Molinet and Vento in \cite{MR3397003}.

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Ricardo Freire, Thyago S. R. Santos. 2025-03-19. The Cauchy problem for nonlinear dispersive models of long internal waves in the presence of the Coriolis force. https://arxiv.org/abs/2503.15480

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