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12 p, 1.9 MB

Non-uniform continuity of the flow map for an evolution equation modeling shallow water waves of moderate amplitude / Duruk-Mutlubaş, Nilay (Istanbul Kemerburgaz University. Department of Basic Sciences) ; Geyer, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Matioc, Bogdan-Vasile (Leibniz Universität Hannover(Germany). Institut für Angewandte Mathematik)
We prove that the flow map associated to a model equation for surface waves of moderate amplitude in shallow water is not uniformly continuous in the Sobolev space Hs with s > 3/2. The main idea is to consider two suitable sequences of smooth initial data whose difference converges to zero in Hs, but such that neither of them is convergent. [...]
2014 - DOI (Digital Object Identifier)

10.1016/j.nonrwa.2013.12.007
Nonlinear Analysis: Real World Applications, Vol. 17 (2014) , p. 322-331

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15 p, 281.6 KB

Orbital stability of solitary waves of moderate amplitude in shallow water / Duruk-Mutlubaş, Nilay (University of Vienna. Faculty of Mathematics) ; Geyer, Anna (University of Vienna. Faculty of Mathematics)
We study the orbital stability of solitary traveling wave solutions of an equation for surface water waves of moderate amplitude in the shallow water regime. Our approach is based on a method proposed by Grillakis, Shatah and Strauss in 1987 [1], and relies on a reformulation of the evolution equation in Hamiltonian form. [...]
2013 - DOI (Digital Object Identifier)

10.1016/j.jde.2013.04.010
Journal of differential equations, Vol. 255 Núm. 2 (2013) , p. 254-263

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