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Degeneracy in the Blasius problem

Keywords: Navier-Stokes equations , Blasius problem , degeneracy , Wang equation , well-posed problem , ill-posed problem

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Abstract:

The Navier-Stokes equations for the boundary layer are transformed, by a similarity transformation, into the ordinary Blasius differential equation which, together with appropriate boundary conditions constitutes the Blasius problem, $$ f'''(eta )+frac{1}{2}f(eta )f''(eta)=0,quad f(0)=0,; f'(0)=0,; f'(infty )=1. $$ The well-posedness of the Navier-Stokes equations is an open problem. We solve this problem, in the case of constant flow in a boundary layer, by showing that the Blasius problem is ill-posed. If the second condition is replaced by $f'(0)=-lambda $, then degeneracy occurs for $0 Keywords Navier-Stokes equations --- Blasius problem --- degeneracy --- Wang equation --- well-posed problem --- ill-posed problem

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