Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 73, Issue 6, Pages 1016-1027Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2016.07.007
Keywords
Navier-Stokes equations; Caputo fractional derivative; Weak solutions; Existence; Optimal controls
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Funding
- National Natural Science Foundation of China [11271309]
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In this paper, we deal with the Navier-Stokes equations with the time -fractional derivative of order alpha is an element of (0, 1), which can be used to simulate anomalous diffusion in fractal media. We firstly give the concept of the weak solutions and establish the existence criterion of weak solutions by means of Galerkin approximations in the case that the dimension n <= 4. Moreover, a complete proof of the uniqueness is given when n = 2. At last we give a sufficient condition of optimal control pairs. (C) 2016 Elsevier Ltd. All rights reserved.
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