8 citations · 8 across the 3 of their papers we have counts for
6 papers
Contour dynamics and global regularity for periodic vortex patches and layers
David M. Ambrose, Fazel Hadadifard, James P. Kelliher
We study vortex patches for the 2D incompressible Euler equations. Prior works on this problem take the support of the vorticity (i.e., the vortex patch) to be a bounded region. We…
Well-posedness and asymptotics of a coordinate-free model of flame fronts
David M. Ambrose, Fazel Hadadifard, J. Douglas Wright
We investigate a coordinate-free model of flame fronts introduced by Frankel and Sivashinsky; this model has a parameter which relates to how unstable the front might be. We fi…
Mass-in-Mass Lattices with Small Internal Resonators
Fazel Hadadifard, J. Douglas Wright
We consider the mass-in-mass (MiM) lattice when the internal resonators are very small. When there are no internal resonators the lattice reduces to a standard Fermi-Pasta-Ulam-Tsi…
On the forced surface quasi-geostrophic equation: Existence of steady states and sharp relaxation rates
Fazel Hadadifard, Atanas G. Stefanov
We consider the asymptotic behavior of the surface quasi-geostrophic equation, subject to a small external force. Under suitable assumptions on the forcing, we first construct the…
Sharp relaxation rates for plane waves of reaction-diffusion systems
Fazel Hadadifard, Atanas G. Stefanov
It is well-known and classical result that spectrally stable traveling waves of a general reaction-diffusion system in one spatial dimension are asymptotically stable with exponent…
On the sharp time decay rates for the 2D generalized quasi-geostrophic equation and the Boussinesq system
Atanas G. Stefanov, Fazel Hadadifard
We compute the sharp time decay rates of the solutions of the IVP for quasi-geostrophic equation and the Boussinesq model, subject to fractional dissipation. Moreover, we explicitl…