Global Weak Solutions for a Shallow Water Equation

2000/04/01 by Adrian Constantin, Luc Molinet · 403 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Complex system #Computer science #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #Thermodynamics #Waves and shallow water

paper · doi:10.1007/s002200050801

published in Communications in Mathematical Physics 211(1), 45-61 (Springer Science and Business Media LLC)

crossref issued 2000/04/01 · crossref published 2000/04/01 · crossref published-print 2000/04/01 · openalex publication_date 2000/04/01 · crossref created 2002/10/06 · crossref deposited 2019/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05 · crossref indexed 2026/08/05

Citations

• Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod
• Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation
• The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
• Wave breaking for nonlinear nonlocal shallow water equations

Cited by

• Numerical simulation of Camassa–Holm peakons by adaptive upwinding
• Equations of Camassa‐Holm type and Jacobi ellipsoidal coordinates
• A blow-up result for the periodic Camassa-Holm equation
• On the Cauchy problem for the Camassa–Holm equation
• Traveling wave solutions of the Camassa–Holm equation
• Orbital stability of solitary waves for a shallow water equation
• Multi-symplectic integration of the Camassa–Holm equation
• Singular limit problem of the Camassa–Holm type equation
• A Note on the analytic solutions of the Camassa–Holm equation
• Global Conservative Solutions of the Camassa–Holm Equation—A Lagrangian Point of View
• Finite propagation speed for 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
• Low-Regularity Solutions of the Periodic Camassa–Holm Equation
• A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation
• GLOBAL CONSERVATIVE MULTIPEAKON SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Convergence of a Finite Difference Scheme for the Camassa–Holm Equation
• A Convergent Finite Difference Scheme for the Camassa–Holm Equation with General H¹ Initial Data
• Global existence of weak solutions to the Camassa-Holm equation
• Existence time for the Camassa-Holm equation and the critical Sobolev index
• A Variational Approach to the Stability of Periodic Peakons
• A convergent numerical scheme for the Camassa--Holm equation based on multipeakons
• Periodic conservative solutions of the Camassa–Holm equation
• Stability for the periodic Camassa-Holm equation
• Camassa–Holm equation [wikipedia]