A factorization theorem for operators occurring in the Stokes, Brinkman and Oseen equations

Suman Kumar Tumuluri and T. Amaranath

Applied Mathematics and Computation, 2016, vol. 276, issue C, 75-79

Abstract: In many physical problems one is faced with solving partial differential equations of the form L1(L1+L2)u=0, where L1 and L2 are linear operators. It is found in many cases that the solution u is of the form u1+u2 where L1u1=0 and (L1+L2)u2=0. In this paper we present sufficient conditions under which such a splitting is possible. Moreover, we give explicit formulae for u1 and u2 for a given u. We also show in some examples where the operators satisfy the sufficient conditions and such a splitting is used extensively. In particular, we find a class of solutions for the unsteady Brinkman and unsteady Oseen equations using the splitting that we propose.

Keywords: Factorization theorem; Stokes flows; The Brinkman equations; The Oseen equations (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:276:y:2016:i:c:p:75-79

DOI: 10.1016/j.amc.2015.11.093

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