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

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  • Tumuluri, Suman Kumar
  • Amaranath, T.

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.

Suggested Citation

  • Tumuluri, Suman Kumar & Amaranath, T., 2016. "A factorization theorem for operators occurring in the Stokes, Brinkman and Oseen equations," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 75-79.
    • Handle: RePEc:eee:apmaco:v:276:y:2016:i:c:p:75-79
    DOI: 10.1016/j.amc.2015.11.093
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