65 research outputs found
The 2D Euler-Poisson System with Spherical Symmetry
This article concerns the global-in-time existence of smooth solutions with
small amplitude to two space dimensional Euler-Poisson system. The main
difficulty lies in the slow time decay of the linear system.
Inspired by Ozawa, Tsutaya, and Tsutsumi's work, we show that such smooth
solutions exist for radially symmetric flows
Passive scalars, moving boundaries, and Newton's law of cooling
We study the evolution of passive scalars in both rigid and moving slab-like
domains, in both horizontally periodic and infinite contexts. The scalar is
required to satisfy Robin-type boundary conditions corresponding to Newton's
law of cooling, which lead to nontrivial equilibrium configurations. We study
the equilibration rate of the passive scalar in terms of the parameters in the
boundary condition and the equilibration rates of the background velocity field
and moving domain.Comment: 27 page
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