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math.AP2025
Exponential blow-up of mild solutions to the fractional Boussinesq equations in the Gevrey class
Wilberclay G. Melo, Cilon Perusato, Thyago S. R. Santos
This work establishes conditions for the existence and uniqueness of local mild solutions to the Boussinesq equations with fractional dissipations in Sobolev-Gevrey spaces. We prov…
math.AP2025
Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations
Simão Correia, Gonçalo Pereira, Thyago S. R. Santos
Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction…
math.AP2025
The Cauchy problem for nonlinear dispersive models of long internal waves in the presence of the Coriolis force
Ricardo Freire, Thyago S. R. Santos
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 prese…