Convergence of the Ostrovsky equation to the Ostrovsky-Hunter one

By Giuseppe Maria Coclite, Lorenzo di Ruvo. 2013

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We consider the Ostrovsky equation, which contains nonlinear dispersive eff?ects. We prove that as the diff?usion parameter tend to zero, the solutions of the dispersive equation converge to discontinuous weak solutions of the Ostrovsky-Hunter equation. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L^p setting.

Subfields: Mathematical Physics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/91238a0e1b257c0920f0badca8a764a480864514