Existence and uniqueness for non-linear singular integral equations used in fluid mechanics

E. G. Ladopoulos; V. A. Zisis

Applications of Mathematics (1997)

  • Volume: 42, Issue: 5, page 345-367
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Ladopoulos, E. G., and Zisis, V. A.. "Existence and uniqueness for non-linear singular integral equations used in fluid mechanics." Applications of Mathematics 42.5 (1997): 345-367. <http://eudml.org/doc/32986>.

@article{Ladopoulos1997,
abstract = {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.},
author = {Ladopoulos, E. G., Zisis, V. A.},
journal = {Applications of Mathematics},
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; equations over finite set of contours; steady incompressible motion; Banach spaces; Hölder conditions; turbomachines},
language = {eng},
number = {5},
pages = {345-367},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence and uniqueness for non-linear singular integral equations used in fluid mechanics},
url = {http://eudml.org/doc/32986},
volume = {42},
year = {1997},
}

TY - JOUR
AU - Ladopoulos, E. G.
AU - Zisis, V. A.
TI - Existence and uniqueness for non-linear singular integral equations used in fluid mechanics
JO - Applications of Mathematics
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 42
IS - 5
SP - 345
EP - 367
AB - 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.
LA - eng
KW - 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; equations over finite set of contours; steady incompressible motion; Banach spaces; Hölder conditions; turbomachines
UR - http://eudml.org/doc/32986
ER -

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