Quasilinear evolution equations in \(L_\mu^P\)-spaces with lower regular initial data (Q1749073)
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scientific article; zbMATH DE number 6868703
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasilinear evolution equations in \(L_\mu^P\)-spaces with lower regular initial data |
scientific article; zbMATH DE number 6868703 |
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Quasilinear evolution equations in \(L_\mu^P\)-spaces with lower regular initial data (English)
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15 May 2018
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Summary: We study the Cauchy problem of the quasilinear evolution equations in \(L_\mu^p\)-spaces. Based on the theories of maximal \(L^p\)-regularity of sectorial operators, interpolation spaces, and time-weighted \(L^p\)-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 \(L^{p, q}\)-spaces with temporal weights.
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0.9173692
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0.9157771
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0.90842545
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