The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this equation with a class of bounded discontinuous solutions. We show that we can replace the Kruzkov-type entropy inequalities by an Oleinik-type estimate and to prove uniqueness via a nonlocal adjoint problem. An implication is that a shock wave in an entropy weak solution to the Ostrovsky-Hunter equation is admissible only if it jumps down in value (like the inviscid Burgers equation).

Oleinik type estimates for the Ostrovsky–Hunter Equation / Coclite, Giuseppe Maria; di Ruvo, L.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 423:1(2015), pp. 162-190. [10.1016/j.jmaa.2014.09.033]

Oleinik type estimates for the Ostrovsky–Hunter Equation

COCLITE, Giuseppe Maria;
2015-01-01

Abstract

The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this equation with a class of bounded discontinuous solutions. We show that we can replace the Kruzkov-type entropy inequalities by an Oleinik-type estimate and to prove uniqueness via a nonlocal adjoint problem. An implication is that a shock wave in an entropy weak solution to the Ostrovsky-Hunter equation is admissible only if it jumps down in value (like the inviscid Burgers equation).
2015
Oleinik type estimates for the Ostrovsky–Hunter Equation / Coclite, Giuseppe Maria; di Ruvo, L.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 423:1(2015), pp. 162-190. [10.1016/j.jmaa.2014.09.033]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/93892
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