L^p-L^q Maximal Regularity for some Operators Associated with\n Linearized Incompressible Fluid-Rigid Body Problems

2017/12/01 by Debayan Maity, Maity, Debayan, Marius Tucsnak +1 · 1 citation
Mathematics · #35Q30 #76D03 #76N10 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1712.00223

openalex publication_date 2017/12/01 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We study an unbounded operator arising naturally after linearizing the system\nmodelling the motion of a rigid body in a viscous incompressible fluid. We show\nthat this operator is \R sectorial in L^q for every q\∈\n(1,\∞), thus it has the maximal L^p-L^q regularity property. Moreover,\nwe show that the generated semigroup is exponentially stable with respect to\nthe L^q norm. Finally, we use the results to prove the global existence for\nsmall initial data, in an L^p-L^q setting, for the original nonlinear\nproblem.\n

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