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

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• 作者：Suman Kumar Tumuluri ^{suman.hcu@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; T. Amaranath ; ^{amaranath.t@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Factorization theorem ; Stokes flows ; The Brinkman equations ; The Oseen equations
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 March 2016
• 年：2016
• 卷：276
• 期：Complete
• 页码：75-79
• 全文大小：261 K

文摘

In many physical problems one is faced with solving partial differential equations of the form L₁(L₁+L₂)u=0,$L_1(L_1+L_2)u=0,$ where L₁ and L₂ are linear operators. It is found in many cases that the solution u   is of the form u₁+u₂$u_1+u_2$ where L₁u₁=0$L_1{u}_1=0$ and (L₁+L₂)u₂=0.$(L_1+L_2)u_2=0.$ 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.