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arXiv · 1604.05147

3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system

Myoungjean Bae·Shangkun Weng
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Abstract

We address the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler-Poisson system in a cylinder supplemented with non small boundary data. A special Helmholtz decomposition of the velocity field is introduced for 3-D axisymmetric flow with a nonzero swirl(=angular momentum density) component. With the newly introduced decomposition, a quasilinear elliptic system of second order is derived from the elliptic modes in Euler-Poisson system for subsonic flows. Due to the nonzero swirl, the main difficulties lie in the solvability of a singular elliptic equation which concerns the angular component of the vorticity in its cylindrical representation, and in analysis of streamlines near the axis $r=0$.

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Myoungjean Bae, Shangkun Weng. 2016-04-18. 3-D axisymmetric subsonic flows with nonzero swirl for the compressible Euler-Poisson system. https://arxiv.org/abs/1604.05147

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