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Full-Text Articles in Physical Sciences and Mathematics
Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang
Examples Of Boundary Layers Associated With The Incompressible Navier-Stokes Equations, Xiaoming Wang
Mathematics and Statistics Faculty Research & Creative Works
The author surveys a few examples of boundary layers for which the Prandtl boundary layer theory can be rigorously validated. All of them are associated with the incompressible Navier-Stokes equations for Newtonian fluids equipped with various Dirichlet boundary conditions (specified velocity). These examples include a family of (nonlinear 3D) plane parallel flows, a family of (nonlinear) parallel pipe flows, as well as flows with uniform injection and suction at the boundary. We also identify a key ingredient in establishing the validity of the Prandtl type theory, i.e., a spectral constraint on the approximate solution to the Navier-Stokes system constructed by …
Asymptotic Analysis Of Singularly Perturbed Abstract Evolution Equations In Banach And Hilbert Spaces, Dialla Konate
Asymptotic Analysis Of Singularly Perturbed Abstract Evolution Equations In Banach And Hilbert Spaces, Dialla Konate
Turkish Journal of Mathematics
In the current paper, we are concerned with the study of abstract linear evolution equations in Banach spaces in which the time derivative term is multiplied by a small parameter, say \epsilon. Such equations arise in the study of radiative transfer and neutron transport in Nuclear Physics. Following works by Krein (cf [9]) and others, Mika (cf [12,13,14,15]) using either the Hilbert method or the Compressed method has shown that the solution of the given singularly perturbed equation may be approximated upto any prescibed order by a sum of two asymptotic expansions that are the outer expansion that is valid …