J. Holmes

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math.AP2020

Continuity of the data-to-solution map for the FORQ equation in Besov Spaces

John Holmes, Feride Tiglay, Ryan Thompson

For Besov spaces $B^s_{p,r}(\rr)$ with $s > max {2 + \frac{1}{p}, \frac{5}{2}}$ , $p \in (1, \infty]$ and $r \in [1, \infty)$ , it is proved that the data-to-solution map for the FORQ equ…

math.AP2020

Non-uniqueness for the ab-family of equations

John Holmes, Rajan Puri

We study the cubic ab-family of equations, which includes both the Fokas-Olver-Rosenau-Qiao (FORQ) and the Novikov (NE) equations. For $a \neq = 0$ , it is proved that there exist initi…

math.AP2016

Well-posedness and Continuity Properties of the Fornberg-Whitham Equation in Besov Spaces

John Holmes, Ryan C. Thompson

In this paper, we prove well-posedness of the Fornberg-Whitham equation in Besov spaces $B_{2, r}^{s}$ in both the periodic and non-periodic cases. This will imply the existence and u…