The existence of a weak solution u(x, t) , in the -sense of J. Le'ray ([7]), is established for the initial-boundary value problem for the Navier-Stokes equations:
[Formula omitted]
The solution is required to satisfy the initial condition u(x, 0) = u[subscript]o (x) for x ɛΩ, and the boundary condition u(x, t) = 0 on ∂Ω x [0, T], where Ω is an open bounded domain in IR[superscript]n, with 2 ≤ n ≤ 4. Galerkin's method is employed to find a weak solution u as the limit of approximate solutions {u[subscript]m} . The convergence of the {u[subscript]m}is guaranteed by some compact embedding theorems, which depend on a priori estimates for the {u[subscript]m} and their fractional time derivatives of order Ƴ, 0<Ƴ<1/4. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/35616 |
| Date | January 1970 |
| Creators | Wei, David Yuen |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
Page generated in 0.0151 seconds