John Holmes, Rajan Puri
Published 2020-02-02Version 1
We study the cubic ab-family of equations, which includes both the Fokas-Olver-Rosenau-Qiao (FORQ) and the Novikov (NE) equations. For $a\neq0$, it is proved that there exist initial data in the Sobolev space $H^s$, $s<3/2$, with non-unique solutions. Multiple solutions are constructed by studying the collision of 2-peakon solutions. Furthermore, we prove the novel phenomenon that for some members of the family, collision between 2-peakons can occur even if the "faster" peakon is in front of the "slower" peakon.
Cauchy problem of nonlinear Schrödinger equation with Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space $W^{s,p}$ for $p<2$
Quasi-geostrophic equations with initial data in Banach spaces of local measures
Finite-time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics
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