TIME-PERIODIC SOLUTION TO A THREE-PHASE MODEL OF VISCOELASTIC FLUID FLOW

This paper is concerned with a three-phase model of viscoelastic fluid flow in RN for N >= 5. We first prove the existence of the time-periodic solution to the integral system in the space of BC(R; LN,infinity(S2)). Then we further show the existence, uniqueness and regularity of the mild solution of the problem. Finally we confirm that such a mild solution is a strong solution in the space of BC(R; LN,infinity(S2)). The proof is based on the compactness analysis with some new development, where a new estimate scheme is artfully constructed.