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arXiv · 2607.18701

Subsonic time-periodic solutions to radially symmetric spiral flows in an annulus

Huimin Yu·Zihao Zhang
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Abstract

We investigate subsonic time-periodic solutions to the radially symmetric non-isentropic Euler system with nonzero angular velocity in an annulus. Under the assumption that the boundary conditions are dissipative on the inner circle and non-dissipative on the outer circle, we establish the existence and stability of time-periodic solutions which are close to steady radially symmetric subsonic spiral flows. It is worth noting that there is no smallness restriction on the background subsonic solutions. The main difficulties arise from the derivative loss caused by the coupling with the radial entropy derivative and the additional zeroth-order terms induced by the nonzero angular velocity in the diagonalized system. One of the key ingredients of the analysis is to rewrite the radial derivative of the entropy as a derivative along the first or fourth characteristic direction. Another one is to control the accumulation of perturbations along characteristic curves by suitably restricting the width of the annulus.

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Huimin Yu, Zihao Zhang. 2026-07-21. Subsonic time-periodic solutions to radially symmetric spiral flows in an annulus. https://arxiv.org/abs/2607.18701

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