On bounded and almost-periodic solutions of certain non-linear evolution equations

1982 ◽  
Vol 37 (2) ◽  
pp. 239-240 ◽  
Author(s):  
A A Pankov
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Linear Evolution ◽  
Non Linear ◽  
Linear Evolution Equations

Periodic Solutions of Non-Linear Evolution Equations in Banach Spaces

1971 ◽  
Vol 23 (1) ◽  
pp. 189-196 ◽  
Author(s):  
Bui An Ton
Keyword(s):  
Periodic Solutions ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Inner Product ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Linear Evolution ◽  
Non Linear ◽  
Linear Evolution Equations

In this paper the theory of Browder [2] and of Lions [3] on periodic solutions of non-linear evolution equations in Banach spaces is put in a more general framework so as to include the Navier-Stokes equations and their variants.An abstract existence theorem is proved in § 1. Applications are given in § 2. The existence of periodic solutions of the Navier-Stokes equations without any restriction on the dimension of the space domain is established. Application of the abstract theorem to the following problem is given:1. Let H be a Hilbert space and (., .)H the inner product in H. Let V and W be two reflexive separable Banach spaces with W ⊂ V ⊂ H. W is dense in V and V is dense in H.

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