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arXiv · 2509.23538

Global dynamics of damped Euler systems with exterior potentials

Young-Pil Choi·Houzhi Tang·Weiyuan Zou
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Abstract

We study the three-dimensional isothermal Euler equations with linear damping and an exterior potential. For sufficiently large damping, we prove global well-posedness for arbitrarily large initial data by combining a parabolic comparison principle with scaled high-order energy estimates ensuring uniform density bounds. In the small-data regime with arbitrary damping, we establish global classical solutions and derive sharp algebraic decay rates via spectral analysis and frequency decomposition, and further prove their optimality under a mild non-degeneracy condition. Finally, for the pressureless damped system, we construct a weighted functional showing that solutions can blow up in finite time when the damping is insufficient, highlighting a qualitative difference from the pressured case.

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Young-Pil Choi, Houzhi Tang, Weiyuan Zou. 2025-09-28. Global dynamics of damped Euler systems with exterior potentials. https://arxiv.org/abs/2509.23538

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