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<p>We establish a novel relationship connecting pressure, curvature, velocity, and gravitational acceleration in two-dimensional steady incompressible fluids with general vorticity under gravitational effects. As an application, we extend the well-posedness theory for two-dimensional stationary gravity flows with vorticity developed by Wang [J Lond Math Soc, 2024, 109(2): e12869]. Our analysis demonstrates that the minimum pressure within the fluid domain is attained precisely on the free surface, thereby establishing a new lower bound for the curvature of the free boundary.</p>

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Curvature bounds in free surface flows with gravity and vorticity

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Fan Zhang

摘要

We establish a novel relationship connecting pressure, curvature, velocity, and gravitational acceleration in two-dimensional steady incompressible fluids with general vorticity under gravitational effects. As an application, we extend the well-posedness theory for two-dimensional stationary gravity flows with vorticity developed by Wang [J Lond Math Soc, 2024, 109(2): e12869]. Our analysis demonstrates that the minimum pressure within the fluid domain is attained precisely on the free surface, thereby establishing a new lower bound for the curvature of the free boundary.