Abstract
We present a necessary and sufficient condition for the convergence of solutions of the incompressible Navier-Stokes equations to that of the Euler equations at vanishing viscosity. Roughly speaking convergence is true in the energy space if and only if the energy dissipation rate of the viscous flows due to the tangential derivatives of the velocity in a thick enough boundary layer, a small quantity in classical boundary layer theory, approaches zero at vanishing viscosity. This improves a previous result of T. Kato (1984) in the sense that we require tangential derivatives only while the total gradient is needed in Kato’s work. However we require a slightly thicker boundary layer. We also improve our previous result where only sufficient conditions were obtained. Moreover we treat more general boundary condition which includes Taylor-Couette type flows. Several applications are presented as well. ∗wang@math.iastate.edu, 1-(515)294-1752 (T), 1-(515)294-5454(F)
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
