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<p>In 1982, Alt, Caffarelli and Friedman [Comm Pure Appl Math, 1982, 35: 29–68] established the existence of the solution to the asymmetric incompressible jet flows. As a continuation of Alt-Caffarelli-Friedman’s work, we investigate the geometric shape of free boundaries of the asymmetric incompressible jet flows in this paper. More precisely, we will first show the strict monotonicity of free boundaries under the monotonicity hypotheses on the nozzle walls. Secondly, if the nozzle walls are convex to the fluid, it is proved that the free boundaries are strictly concave to the fluid. Finally, as a by-product, the optimal regularity of free boundaries at the separation points can be established.</p>

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The shape of free boundary for the asymmetric incompressible jet flows

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Xiaohui Wang,
  • Haiqian Zhou

摘要

In 1982, Alt, Caffarelli and Friedman [Comm Pure Appl Math, 1982, 35: 29–68] established the existence of the solution to the asymmetric incompressible jet flows. As a continuation of Alt-Caffarelli-Friedman’s work, we investigate the geometric shape of free boundaries of the asymmetric incompressible jet flows in this paper. More precisely, we will first show the strict monotonicity of free boundaries under the monotonicity hypotheses on the nozzle walls. Secondly, if the nozzle walls are convex to the fluid, it is proved that the free boundaries are strictly concave to the fluid. Finally, as a by-product, the optimal regularity of free boundaries at the separation points can be established.