2014/03/06 by Myong‐Hwan Ri, Ri, Myong-Hwan, Reinhard Frawig +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1403.1380
openalex publication_date 2014/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study resolvent estimate and maximal regularity of the Stokes operator in Lq-spaces with exponential weights in the axial directions of unbounded cylinders of \mathbb Rn,n≥ 3. For straights cylinders we obtain these results in Lebesgue spaces with exponential weights in the axial direction and Muckenhoupt weights in the cross-section. Next, for general cylinders with several exits to infinity we prove that the Stokes operator in Lq-spaces with exponential weight along the axial directions generates an exponentially decaying analytic semigroup and has maximal regularity. The proofs for straight cylinders use an operator-valued Fourier multiplier theorem and techniques of unconditional Schauder decompositions based on the \mathcal 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 result for the case without exponential weight.