Funkcialaj Ekvacioj
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Resolvent Estimates for the Linearized Compressible Navier-Stokes Equation in an Infinite Layer
Yoshiyuki Kagei
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2007 Volume 50 Issue 2 Pages 287-337

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Abstract

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.

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© 2007 by the Division of Functional Equations, The Mathematical Society of Japan
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