Global Regularity to Incompressible Viscoelastic System With a Class of Large Initial Data
Abstract
The global existence of solutions to incompressible viscoelastic flows has been a longstanding open problem, even for the global weak solution. Under some special structure ("div-curl" condition) the global small smooth solution was obtained in llzhou, cz. However, the result with large initial data remains unknown up to now, and it is studied in this paper. We shall put forward a new structure: the cone-condition and then derive the global smooth solution to 3D incompressible viscoelastic system with a class of large initial data. The key is to gain an angle quantity in the estimate of nonlinear terms by restricting the solution to a cone.
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