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Convergence of the Equations for a Maxwell Fluid
Author(s) -
Payne L. E.,
Straughan B.
Publication year - 1999
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00128
Subject(s) - convergence (economics) , maxwell's equations , relaxation (psychology) , mathematics , mathematical analysis , zero (linguistics) , flow (mathematics) , a priori and a posteriori , viscoelasticity , fluid dynamics , stokes flow , type (biology) , physics , mechanics , geometry , thermodynamics , psychology , social psychology , linguistics , philosophy , ecology , epistemology , biology , economics , economic growth
The equations for the flow of a viscoelastic fluid of the Maxwell type are analyzed in a linear approximation. First, we establish that the solution depends continuously on changes in the relaxation time. Next, we investigate how the solution to the linearized Maxwell system converges to the solution to Stokes flow as the relaxation time tends to zero. Convergence in different measures is examined and specific a priori bounds are derived.