Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
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Myong-Hwan Ri
Abstract
We study resolvent estimates and maximal regularity of the Stokes operator in Lq-spaces with exponential weights in the axial directions of unbounded cylinders of ℝn, n ≥ 3. For a straight cylinder we use exponential weights in the axial direction and Muckenhoupt weights in the cross-section. Next, for cylinders with several exits to infinity we prove that the Stokes operator in Lq-spaces with exponential weights generates an exponentially decaying analytic semigroup and has maximal regularity. The proof for straight cylinders uses an operator-valued Fourier multiplier theorem and unconditional Schauder decompositions based on the ℛ-boundedness of the family of solution operators for a system in the cross-section of the cylinder parametrized by the phase variable of the one-dimensional partial Fourier transform. For general cylinders we use cut-off techniques based on the result for straight cylinders and the case without exponential weight.
Funding source: 2012 CAS-TWAS Postdoctoral Fellowship
Award Identifier / Grant number: 3240267229
Funding source: CAS (Chinese Academy of Sciences)
Funding source: TWAS (The World Academy of Sciences)
The first author is grateful to Professor Ping Zhang for inviting him and CAS (Chinese Academy of Sciences) and TWAS (The World Academy of Sciences) for financial support.
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
- Strong solutions of the Boussinesq system in exterior domains
- Some stability results on global solutions to the Navier–Stokes equations
- The Navier–Stokes–Fourier system: From weak solutions to numerical analysis
- Global regularity for a model Navier–Stokes equations on ℝ3
- The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain
Articles in the same Issue
- Frontmatter
- Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders
- Strong solutions of the Boussinesq system in exterior domains
- Some stability results on global solutions to the Navier–Stokes equations
- The Navier–Stokes–Fourier system: From weak solutions to numerical analysis
- Global regularity for a model Navier–Stokes equations on ℝ3
- The steady Navier–Stokes problem with the inhomogeneous Navier-type boundary conditions in a 2D multiply-connected bounded domain
