Axisymmetric flow of ideal fluid moving in a narrow domain: A study of the axisymmetric hydrostatic Euler equations

@article{Strain2016AxisymmetricFO,
  title={Axisymmetric flow of ideal fluid moving in a narrow domain: A study of the axisymmetric hydrostatic Euler equations},
  author={Robert M. Strain and Tak Kwong Wong},
  journal={Journal of Differential Equations},
  year={2016},
  volume={260},
  pages={4619-4656}
}
Abstract In this article we will introduce a new model to describe the leading order behavior of an ideal and axisymmetric fluid moving in a very narrow domain. After providing a formal derivation of the model, we will prove the well-posedness and provide a rigorous mathematical justification for the formal derivation under a new sign condition. Finally, a blowup result regarding this model will be discussed as well. 

References

SHOWING 1-10 OF 17 REFERENCES
Remarks on the derivation of the hydrostatic Euler equations
Abstract The motion of an inviscid incompressible fluid between two horizontal plates is studied in the limit when the plates are infinitesimally close. The convergence of the solutions of the Euler
Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain
Abstract We address the question of well-posedness in spaces of analytic functions for the Cauchy problem for the hydrostatic incompressible Euler equations (inviscid primitive equations) on domains
On the Hs Theory of Hydrostatic Euler Equations
In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence and uniqueness of Hs solutions under the local Rayleigh condition. This
Characterization and Regularity for Axisymmetric Solenoidal Vector Fields with Application to Navier-Stokes Equation
TLDR
It is shown that, to characterize the regularity of a divergence free axisymmetric vector field in terms of the swirling components, an extra set of pole conditions is necessary to give a full description of theRegularity.
Homogeneous hydrostatic flows with convex velocity profiles
We consider the Euler equations of an incompressible homogeneous fluid in a thin two-dimensional layer , , with slip boundary conditions at z = 0, and periodic boundary conditions in x. After
On the derivation of homogeneous hydrostatic equations
In this paper we study the derivation of homogeneous hydrostatic equations starting from 2D Euler equations, following for instance [2,9]. We give a convergence result for convex profiles and a
Ill-posedness of the Hydrostatic Euler and Navier–Stokes Equations
We prove that the linearization of the hydrostatic Euler equations at certain parallel shear flows is ill-posed. The result also extends to the hydrostatic Navier–Stokes equations with a small
On the nonlinear instability of Euler and Prandtl equations
In this paper we give examples of nonlinearly unstable solutions of Euler equations in the whole space ℝ2, the half space ℝ × ℝ+, the periodic strip ℝ × , the strip ℝ × [−1,1], and the periodic torus
Finite-Time Blowup for the Inviscid Primitive Equations of Oceanic and Atmospheric Dynamics
In an earlier work we have shown the global (for all initial data and all time) well-posedness of strong solutions to the three-dimensional viscous primitive equations of large scale oceanic and
Blowup of Solutions of the Hydrostatic Euler Equations
In this paper we prove that for a certain class of initial data, smooth solutions of the hydrostatic Euler equations blow up in finite time.
...
1
2
...