1 citations · 2 across the 2 of their papers we have counts for
5 papers
Weak diffeomorphisms and solutions to conservation laws
John Holmes, Barbara Keyfitz, Feride Tiglay
Evolution equations which describe the changes in a velocity field over time have been classically studied within the Eulerian or Lagrangian frame of reference. Classically, these…
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 , and , it is proved that the data-to-solution map for the FORQ equ…
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 , it is proved that there exist initi…
Nonuniform dependence on initial data for compressible gas dynamics: The Cauchy problem on
John Holmes, Barbara Lee Keyfitz, Feride Tiglay
The Cauchy problem for the two dimensional compressible Euler equations with data in the Sobolev space is known to have a unique solution of the same Sobolev cla…
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 in both the periodic and non-periodic cases. This will imply the existence and u…