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Theorem 2.2 implies that problem (1.8 - 1.13) admits a unique global strong solution.
Yamaguchi [3] considered the global strong solution in a bounded domain with small initial data.
For the autonomous case, in [12], Cai and Jiu proved that Cauchy problem (1) possesses global strong solutions when (betageqfrac{7}{2}), and the global strong solution is unique when (frac{7}{2}leqbetaleq5).
The existence and uniqueness of global strong solutions and global weak solutions to the closed loop control system are obtained.
The existence and uniqueness of a global strong solution for the problem were obtained by means of the Galerkin method.
Moreover, it has global strong solutions and also admits finite time blow-up solutions [17, 18, 20, 21].
They established that the strong solution exists when (beta> 3), and the global strong solution is unique when (3
More interestingly, there are a rich variety of global strong solutions and blow-up solutions [8 10].
Sun and Zhang [20] obtained the existence of global strong solutions to the initial boundary value problem.
The system also has global strong solutions which blow-up in finite time [19, 21, 22] and a global weak solution [23].
By using Galerkin's method, Fukuda and Tsutsumi [14] first studied the coupled KGS system and obtained the existence of global strong solutions.
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