Quasilinear Evolution Equations in LμP-Spaces with Lower Regular Initial Data
Keyword(s):
We study the Cauchy problem of the quasilinear evolution equations in Lμp-spaces. Based on the theories of maximal Lp-regularity of sectorial operators, interpolation spaces, and time-weighted Lp-spaces, we establish the local posedness for a class of abstract quasilinear evolution equations with lower regular initial data. To illustrate our results, we also deal with the second-order parabolic equations and the Navier-Stokes equations in Lp,q-spaces with temporal weights.
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1992 ◽
Vol 95
(1)
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pp. 33-74
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2009 ◽
pp. 213-222
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2014 ◽
Vol 257
(2)
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pp. 311-350
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2017 ◽
Vol 35
(2)
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pp. 127
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2018 ◽
Vol 232
(2)
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pp. 557-590
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Keyword(s):
2016 ◽
Vol 36
(5)
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pp. 1419-1432
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