On well-posedness of semilinear Rayleigh-Stokes problem with fractional derivative on ℝ
N
Keyword(s):
Blow Up
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Abstract We are devoted to the study of a semilinear time fractional Rayleigh-Stokes problem on ℝ N , which is derived from a non-Newtonain fluid for a generalized second grade fluid with Riemann-Liouville fractional derivative. We show that a solution operator involving the Laplacian operator is very effective to discuss the proposed problem. In this paper, we are concerned with the global/local well-posedness of the problem, the approaches rely on the Gagliardo-Nirenberg inequalities, operator theory, standard fixed point technique and harmonic analysis methods. We also present several results on the continuation, a blow-up alternative with a blow-up rate and the integrability in Lebesgue spaces.
2018 ◽
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(05)
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pp. 1850032
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2006 ◽
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pp. 1072-1080
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pp. 924-944
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pp. 553-572
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pp. 1533-1546
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2013 ◽
Vol 264
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pp. 163-177
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2018 ◽
Vol 75
(7)
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pp. 2243-2258
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Keyword(s):