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The Linearized 2D Inviscid Shallow Water Equations in a Rectangle: Boundary Conditions and Well-Posedness

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Abstract

We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference velocities (u 0, v 0) and reference height \({\phi_0}\) (sub- or super-critical flow at each part of the boundary).

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Authors and Affiliations

  1. Department of Mathematics, Indiana University Bloomington, 831 East Third Street, Rawles Hall, Bloomington, IN, 47405, USA

    Aimin Huang & Roger Temam

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  1. Aimin Huang
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  2. Roger Temam
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Correspondence to Roger Temam.

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Communicated by C. Le Bris

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Huang, A., Temam, R. The Linearized 2D Inviscid Shallow Water Equations in a Rectangle: Boundary Conditions and Well-Posedness. Arch Rational Mech Anal 211, 1027–1063 (2014). https://doi.org/10.1007/s00205-013-0702-0

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