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The Case of Symmetric Two-Dimensional Domains: General Outflow Condition

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The Steady Navier-Stokes System

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

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Abstract

In this chapter, we demonstrate that in a certain class of symmetric two-dimensional domains, Hopf’s lemma remains valid even when the strict outflow condition (3.2.12) is not satisfied. Instead, it is sufficient to satisfy the necessary general outflow condition (3.2.11).

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Notes

  1. 1.

    This formula is a two-dimensional version of the well-known identity

    $$\displaystyle \begin{aligned} (\mathbf{u}\cdot\nabla)\mathbf{u}=\nabla\big(\frac{1}{2}|\mathbf{u}|{}^2\big)-\mathbf{u}\times\mathrm{curl}\, \mathbf{u}. \end{aligned}$$

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, China

    Mikhail Korobkov

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Mikhail Korobkov

  3. Faculty of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

    Konstantin Pileckas

  4. Società Nazionale di Scienze, Lettere e Arti in Napoli, Naples, Italy

    Remigio Russo

Authors
  1. Mikhail Korobkov
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  2. Konstantin Pileckas
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  3. Remigio Russo
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Korobkov, M., Pileckas, K., Russo, R. (2024). The Case of Symmetric Two-Dimensional Domains: General Outflow Condition. In: The Steady Navier-Stokes System. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-50898-1_4

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