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We study a family of equations defined on the space of tensor densities of weight λ on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the… (More)

- Ralph Saxton, Feride Tiglay
- SIAM J. Math. Analysis
- 2006

This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a… (More)

- Feride Tiglay
- 2005

Abstract.We prove that the periodic initial value problem for the modified Hunter-Saxton equation is locally well-posed for initial data in the space of continuously differentiable functions on the… (More)

It is shown that if a classical solution $(u, n)$ of
the modified Euler-Poisson equation (mEP) in one space dimension
is such that $u$, $u_x$ and $n$ are initially decaying exponentially
and for… (More)

The Cauchy problem for the two dimensional compressible Euler equations with data in the Sobolev space $H^s(\mathbb R^2)$ is known to have a unique solution of the same Sobolev class for a short… (More)

- John Holmes, Feride Tiglay
- 2018

The Cauchy problem for the Hunter–Saxton equation is known to be locally well posed in Besov spaces $$B^s_{2,r} $$B2,rs on the circle. We prove that the data-to-solution map is not uniformly… (More)

- Feride Tiglay
- 2015

We prove the existence and uniqueness of conservative weak solutions of the periodic Cauchy problem for an integrable evolution equation from mathematical physics. Our method is to first prove the… (More)

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 depends… (More)

- John Holmes, Barbara L. Keyfitz, Feride Tiglay
- SIAM J. Math. Analysis
- 2018

The Cauchy problem for the two-dimensional compressible Euler equations with data in the Sobolev space $H^s(\mathbb R^2)$ is known to have a unique solution of the same Sobolev class for a short… (More)

- Feride Tiglay
- 2004