On the blow-up rate and the blow-up set of breaking waves for a shallow water equation

2000/01/01 by Adrian Constantin, Joachim Escher · 295 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Bounded function #Breaking wave #Class (philosophy) #Geometry #Gravitational singularity #Mathematical analysis #Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Physics #Point (geometry) #Set (abstract data type) #Wave equation #Wave propagation #Waves and shallow water

paper · doi:10.1007/pl00004793

published in Mathematische Zeitschrift 233(1), 75-91 (Springer Science and Business Media LLC)

crossref issued 2000/01/01 · crossref published 2000/01/01 · crossref published-print 2000/01/01 · openalex publication_date 2000/01/01 · crossref created 2006/02/17 · crossref deposited 2019/05/23 · openalex created_date 2025/10/10 · crossref indexed 2026/06/17 · openalex updated_date 2026/07/23

Citations

• On the Inverse Spectral Problem for the Camassa–Holm Equation
• Solitons in the Camassa-Holm shallow water equation
• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Wave breaking for nonlinear nonlocal shallow water equations
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation

Cited by

• Geodesic flow on the diffeomorphism group of the circle
• Classical solutions of the periodic Camassa—Holm equation
• Numerical simulation of Camassa–Holm peakons by adaptive upwinding
• A blow-up result for the periodic Camassa-Holm equation
• Traveling wave solutions of the Camassa–Holm equation
• Initial Boundary Value Problems of the Camassa–Holm Equation
• Blow-up, blow-up rate and decay of the solution of the weakly dissipative Camassa-Holm equation
• Global existence of weak solutions to the Camassa-Holm equation
• Existence of permanent and breaking waves for a shallow water equation: a geometric approach
• A Variational Approach to the Stability of Periodic Peakons
• Periodic conservative solutions of the Camassa–Holm equation
• Stability for the periodic Camassa-Holm equation
• Camassa–Holm equation [wikipedia]