Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In many physical problems one is faced with solving partial differential equations of the form 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 u 1 + u 2 where L 1 u 1 = 0 and ( L 1 + L 2 ) u 2 = 0 .   present sufficient conditions under which such a splitting is possible. Moreover,  give explicit formulae for u1 and u2 for a given u.  also show in some examples where the operators satisfy the sufficient conditions and such a splitting is used extensively. In particular,  find a class of solutions for the unsteady Brinkman and unsteady Oseen equations using the splitting that  propose.
['Suman Kumar Tumuluri', 'T. Amaranath']
I am writing a research paper on a idea A factorization theorem for operators occurring in the Stokes, Brinkman and Oseen equations
[{"from": "human", "value": "I am writing a research paper on a idea A factorization theorem for operators occurring in the Stokes, Brinkman and Oseen equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In many physical problems one is faced with solving partial differential equations of the form 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 u 1 + u 2 where L 1 u 1 = 0 and ( L 1 + L 2 ) u 2 = 0 .   present sufficient conditions under which such a splitting is possible. Moreover,  give explicit formulae for u1 and u2 for a given u.  also show in some examples where the operators satisfy the sufficient conditions and such a splitting is used extensively. In particular,  find a class of solutions for the unsteady Brinkman and unsteady Oseen equations using the splitting that  propose."}]