Positive Solutions of the Falkner-Skan Equation Arising in the Boundary Layer Theory

• Autores: K. Q. Lan, G. C. Yang
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 51, Nº 3, 2008, págs. 386-398
• Idioma: inglés
• DOI: 10.4153/cmb-2008-039-7
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• Resumen

  • The well-known Falkner-Skan equation is one of the most important equations in laminar boundary layer theory and is used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies of angles related to lambda pi/2, where lambda \in {mathbb R} is a parameter involved in the equation. It is known that there exists lambda* < 0 such that the equation with suitable boundary conditions has at least one positive solution for each lambda \ge lambda* and has no positive solutions for lambda < lambda*. The known numerical result shows lambda* = -0.1988. In this paper, lambda* \in [-0.4,-0.12] is proved analytically by establishing a singular integral equation which is equivalent to the Falkner-Skan equation. The equivalence result provides new techniques to study properties and existence of solutions of the Falkner-Skan equation.