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A Remark on the Existence of 2-D Steady Navier–Stokes Flow in Bounded Symmetric Domain Under General Outflow Condition

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Let Ω be a 2-dimensional bounded domain, symmetric with respect to the x2-axis. The boundary has several connected components, intersecting the x2-axis. The boundary value is symmetric with respect to the x2-axis satisfying the general outflow condition. The existence of the symmetric solution to the steady Navier–Stokes equations was established by Amick [2] and Fujita [4]. Fujita [4] proved a key lemma concerning the solenoidal extension of the boundary value by virtual drain method. In this note, we give a different proof via elementary approach by means of the stream function.

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Communicated by H. Fujita

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Morimoto, H. A Remark on the Existence of 2-D Steady Navier–Stokes Flow in Bounded Symmetric Domain Under General Outflow Condition. J. math. fluid mech. 9, 411–418 (2007). https://doi.org/10.1007/s00021-005-0206-2

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  • DOI: https://doi.org/10.1007/s00021-005-0206-2

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