6533b852fe1ef96bd12aa370

RESEARCH PRODUCT

ASYMPTOTIC ANALYSIS OF THE LINEARIZED NAVIER–STOKES EQUATION ON AN EXTERIOR CIRCULAR DOMAIN: EXPLICIT SOLUTION AND THE ZERO VISCOSITY LIMIT

Marco SammartinoRussel E. CaflischMaria Carmela Lombardo

subject

Asymptotic analysisApplied MathematicsMathematical analysisAsymptotic analysis; Boundary layer; Explicit solutions; Navier-Stokes equations; Stokes equations; Zero viscosity; Mathematics (all); Analysis; Applied MathematicsMathematics::Analysis of PDEsAnalysiStokes equationDomain (mathematical analysis)Navier-Stokes equationPhysics::Fluid DynamicsSobolev spaceAsymptotic analysiBoundary layersymbols.namesakeBoundary layerSquare rootExplicit solutionInviscid flowStokes' lawsymbolsMathematics (all)Zero viscosityNavier–Stokes equationsAnalysisMathematics

description

In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc.

yearjournalcountryeditionlanguage
2001-01-31Communications in Partial Differential Equations
https://doi.org/10.1081/pde-100001758