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Periodic Solutions of Non-Linear Evolution Equations in Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Bui An Ton
Bui An Ton*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 1 , February 1971 , pp. 189 - 196
Copyright
Copyright © Canadian Mathematical Society 1971

References

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