On the Steady-state Solutions of the Navier- Stokes Equations, Iii
نویسنده
چکیده
C o n t e n t s Page I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 7 . N o t a t i o n a n d def ini t ions; p r e l i m i n a r y e s t ima t e s ; t h e r e p r e s e n t a t i o n f o r m u l a . . . . 201 2. A priori e s t i m a t i o n of t h e Dir ichle t I n t e g r a l . . . . . . . . . . . . . . . . . . 205 2 a) E s t i m a t i o n of t h e Dir ich le t I n t e g r a l in a b o u n d e d region . . . . . . . . . . 208 2 b) E s t i m a t i o n of t h e Dir ich le t I n t e g r a l in a n ex te r io r region; case of zero o u t f l u x 211 2 c) E s t i m a t i o n of t h e Di r i ch le t I n t e g r a l in a n ex t e r io r region; genera l case . . . . 213 3. A pr ior i e s t i m a t i o n of t he so lu t ion . . . . . . . . . . . . . . . . . . . . . . 215 3 a) E s t i m a t i o n of t he so lu t ion in a b o u n d e d reg ion . . . . . . . . . . . . . . 218 3 b) E s t i m a t i o n of t h e so lu t ion in a n ex te r io r reg ion . . . . . . . . . . . . . . 219 4. B e h a v i o u r a t in f in i ty ; t h e r e p r e s e n t a t i o n f o r m u l a . . . . . . . . . . . . . . . 223 5. E x i s t e n c e t h e o r e m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 5 a) E x i s t e n c e of a so lu t ion in a f in i te reg ion . . . . . . . . . . . . . . . . . 226 5 b) E x i s t e n c e of a so lu t ion in a n ex te r io r r eg ion . . . . . . . . . . . . . . . 227 6. R e m a r k s on t he p reced ing sect ions; a n e x a m p l e . . . . . . . . . . . . . . . . 228 7. T r a n s i t i o n to zero R e y n o l d s ' N u m b e r . . . . . . . . . . . . . . . . . . . . 231 7 a) T r a n s i t i o n to zero R e y n o l d ' N u m b e r ; case of a b o u n d e d region . . . . . . . . 231 7 b) T r a n s i t i o n to zero R e y n o l d s ' N u m b e r ; ex te r io r reg ion . . . . . . . . . . . . 234 7 e) T r a n s i t i o n of t h e force e x e r t e d on a f lu id in te r face . . . . . . . . . . . . . 240 8. U n i q u e n e s s a n d c o n t i n u o u s dependence . . . . . . . . . . . . . . . . . . . . 241
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