$L^p$-$L^q$ Maximal Regularity for some Operators associated with Linearized Incompressible Fluid-Rigid Body Problems
Language
en
Article de revue
This item was published in
Contemporary mathematics. 2018
American Mathematical Society
English Abstract
We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\mathcal{R}$ sectorial in $L^q$ for every ...Read more >
We study an unbounded operator arising naturally after linearizing the system modelling the motion of a rigid body in a viscous incompressible fluid. We show that this operator is $\mathcal{R}$ sectorial in $L^q$ for every $q \in (1,\infty)$, thus it has the maximal $L^p$-$L^q$ regularity property. Moreover, we show that the generated semigroup is exponentially stable with respect to the $L^q$ norm. Finally, we use these results to prove the global existence for small initial data, in an $L^p$-$L^q$ setting, for the original nonlinear problem.Read less <
English Keywords
Maximal $L^p$ regularity
Fluid Structure interaction
Incompressible flow
Origin
Hal imported