Funkcialaj Ekvacioj
Print ISSN : 0532-8721
Resolvent Estimates for the Linearized Compressible Navier-Stokes Equation in an Infinite Layer
Yoshiyuki Kagei
Author information

2007 Volume 50 Issue 2 Pages 287-337


The resolvent problem of the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 × (0,a), n ≥ 2, under the no slip boundary condition for the momentum. It is proved that the linearized operator is sectorial in W1,p × Lp for 1 < p < ∞. The Lp estimates for the resolvent are established for all 1 ≤ p ≤ ∞. The estimates for the high frequency part of the resolvent are also derived, which lead to the exponential decay of the corresponding part of the semigroup.

Information related to the author
© 2007 by the Division of Functional Equations, The Mathematical Society of Japan
Previous article Next article