Abstract
We consider the Navier-Stokes equations in half-space and in L p space with Muckenhoupt weight and show the \(L^{p} - L^{q}\) estimates of Stokes semigroup with \(\langle x'\rangle ^{s_{1}}\langle x_{n}\rangle ^{s_{n}}\) type weight. Finally as the application of the weighted \(L^{p} - L^{q}\) estimates, we shall obtain the weighted asymptotic behavior of the solution to the Navier-Stokes equations.
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Dedicated to Professor Yoshihiro Shibata on the occasion of his sixtieth birthday
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This research was partly supported by JSPS Grant-in-Aid for Scientific Research (C) 225-40202.
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Kobayashi, T., Kubo, T. (2016). Weighted L p − L q Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations. In: Amann, H., Giga, Y., Kozono, H., Okamoto, H., Yamazaki, M. (eds) Recent Developments of Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0939-9_18
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DOI: https://doi.org/10.1007/978-3-0348-0939-9_18
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