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Erratum: On the two-dimensional sloshing problem.

Vladimir Kozlov, Nikolay Kuznetsov, Oleg Motygin

    Proceedings. Mathematical, Physical, and Engineering Sciences
    |June 25, 2014
    PubMed
    Summary
    This summary is machine-generated.

    This study provides a correct proof for two-dimensional sloshing problems, confirming the fundamental eigenvalue is simple and the stream function can be non-negative. The new proof relies on stricter water domain assumptions, including John's condition.

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    Area of Science:

    • Fluid dynamics
    • Mathematical physics

    Context:

    • The two-dimensional sloshing problem is a fundamental topic in fluid dynamics.
    • Previous proofs regarding the properties of the fundamental eigenvalue and stream function had limitations.
    • The article corrects assertions made in a previous publication (DOI: 10.1098/rspa.2004.1303).

    Purpose:

    • To provide a correct and rigorous proof for key assertions about the two-dimensional sloshing problem.
    • To establish the simplicity of the fundamental eigenvalue.
    • To demonstrate that the corresponding stream function can be non-negative.

    Summary:

    • A correct proof is presented for the two-dimensional sloshing problem.
    • The fundamental eigenvalue is proven to be simple.
    • The stream function associated with the fundamental eigenvalue can be chosen to be non-negative over the water domain.
    • The new proof requires the water domain to satisfy John's condition, a stricter assumption than previously used.

    Impact:

    • This work clarifies fundamental properties of fluid sloshing.
    • The corrected proofs enhance the reliability of theoretical models in fluid dynamics.
    • Satisfying John's condition provides a more robust framework for analyzing sloshing phenomena.