245 research outputs found
Existence of radial global smooth solutions to the pressureless Euler-Poisson equations with quadratic confinement
We consider the pressureless Euler-Poisson equations with quadratic
confinement. For spatial dimension , we give a necessary and
sufficient condition for the existence of radial global smooth solutions, which
is formulated explicitly in terms of the initial data. This condition appears
to be much more restrictive than the critical-threshold conditions commonly
seen in the study of Euler-type equations. To obtain our results, the key
observation is that every characteristic satisfies a periodic ODE system, and
the existence of global smooth solution requires the period of every
characteristic to be identical
Uniform regularity in the random space and spectral accuracy of the stochastic Galerkin method for a kinetic-fluid two-phase flow model with random initial inputs in the light particle regime
We consider a kinetic-fluid model with random initial inputs which describes disperse two-phase flows. In the light particle regime, using energy estimates, we prove the uniform regularity in the random space of the model for random initial data near the global equilibrium in some suitable Sobolev spaces, with the randomness in the initial particle distribution and fluid velocity. By hypocoercivity arguments, we prove that the energy decays exponentially in time, which means that the long time behavior of the solution is insensitive to such randomness in the initial data. Then we consider the generalized polynomial chaos stochastic Galerkin method (gPC-sG) for the same model. For initial data near the global equilibrium and smooth enough in the physical and random spaces, we prove that the gPC-sG method has spectral accuracy, uniformly in time and the Knudsen number, and the error decays exponentially in time
Global minimizers of a large class of anisotropic attractive-repulsive interaction energies in 2D
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