The nonlinear 2D supercritical inviscid shallow water equations in a rectangle

Article type: Research Article

Authors: Huang, Aimin^a | Petcu, Madalina^{b; c} | Temam, Roger^{a; *}

Affiliations: [a] The Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN, USA. E-mails: aimhuang@indiana.edu, temam@indiana.edu | [b] Laboratoire de Mathématiques et Applications, Université de Poitiers, Futuroscope Chasseneuil cedex, France. E-mail: Madalina.Petcu@math.univ-poitiers.fr | [c] The Institute of Mathematics of the Romanian Academy, Bucharest, Romania

Correspondence: [*] Corresponding author: Roger Temam, The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 East Third Street, Rawles Hall, Bloomington, IN 47405, USA. E-mail: temam@indiana.edu.

Abstract: In this article we consider the inviscid two-dimensional shallow water equations in a rectangle. The flow occurs near a stationary solution in the so called supercritical regime and we establish short term existence of smooth solutions for the corresponding initial and boundary value problem.

Keywords: shallow water equations, inviscid flow, initial and boundary value problems

DOI: 10.3233/ASY-151293

Journal: Asymptotic Analysis, vol. 93, no. 3, pp. 187-218, 2015