94 citations · 117 across the 8 of their papers we have counts for
10 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…
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…
Nonuniform dependence on initial data for compressible gas dynamics: The periodic Cauchy problem
Barbara Lee Keyfitz, Feride Tiglay
We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that…
The periodic Cauchy problem for Novikov's equation
Feride Tiglay
We study the periodic Cauchy problem for an integrable equation with cubic nonlinearities introduced by V. Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, Novikov'…
Generalized Euler-Poincaré equations on Lie groups and homogeneous spaces, orbit invariants and applications
Feride Tiglay, Cornelia Vizman
We develop the necessary tools, including a notion of logarithmic derivative for curves in homogeneous spaces, for deriving a general class of equations including Euler-Poincaré eq…