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Abstract Let the viscosity for the 2D steady Navier‐Stokes equations in the region and with no slip boundary conditions at . For , we justify the validity of the steady Prandtl layer expansion for scaled Prandtl layers, including the celebrated Blasius boundary layer. Our uniform estimates in ε are achieved through a fixed‐point scheme:for solving the Navier‐Stokes equations, where are the tangential and normal velocities at , DNS stands for of the vorticity equation for the normal velocityv, and the compatibility ODE for at .
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The Morse index theorem for mechanical systems with reflections
Abstract We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
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- Award ID(s):
- 2054424
- PAR ID:
- 10519609
- Publisher / Repository:
- IOPScience
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 37
- Issue:
- 8
- ISSN:
- 0951-7715
- Page Range / eLocation ID:
- 085006
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1361-6544/ad5636
