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Article

Ladopoulos, E. G. ; Zisis, V. A.
Existence and uniqueness for non-linear singular integral equations used in fluid mechanics. (English). Applications of Mathematics, vol. 42 (1997), issue 5, pp. 345-367
MSC: 45E05, 45G05, 65L10, 65R20, 76B99, 76M99 | MR 1467554 | Zbl 0906.76076 | DOI: 10.1023/A:1023058024885
Keywords:
non-linear singular integral equations; existence and uniqueness theorems; Banach spaces; Hölder conditions; fluid mechanics; equations over finite set of contours; steady incompressible motion; turbomachines
Summary:
Non-linear singular integral equations are investigated in connection with some basic applications in two-dimensional fluid mechanics. A general existence and uniqueness analysis is proposed for non-linear singular integral equations defined on a Banach space. Therefore, the non-linear equations are defined over a finite set of contours and the existence of solutions is investigated for two different kinds of equations, the first and the second kind. Moreover, the existence of solutions is further studied for non-linear singular integral equations over a finite number of arbitrarily ordered arcs. An application to fluid mechanics theory is finally given for the determination of the form of the profiles of a turbomachine in two-dimensional flow of an incompressible fluid.
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