2134/4428 Maureen McIver Maureen McIver An example of non-uniqueness in the two-dimensional linear water wave problem Loughborough University 2009 untagged Mathematical Sciences not elsewhere classified 2009-04-01 13:10:56 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/An_example_of_non-uniqueness_in_the_two-dimensional_linear_water_wave_problem/9386501 An example of non-uniqueness in the two-dimensional, linear water wave problem is obtained by constructing a potential which does not radiate any waves to infinity and whose streamline pattern represents the flow around two surface-piercing bodies. The potential is constructed from two wave sources which are positioned in the free surface in such a way that the waves radiated from each source cancel at infinity. A numerical calculation of the streamline pattern indicates that there are at least two streamlines which represent surface-piercing bodies, each of which encloses a source point. A proof of the existence of these lines is then given.