Global strong solutions for equations related to the incompressible viscoelastic fluids with a class of large initial data

We investigate the global strong solutions for a system related to the incompressible viscoelastic fluids of Oldroyd-B type with a class of large initial data E0=[E0,ij]N×NE0=[E0,ij]N×N, v0=[v01,…,v0N]⊤v0=[v01,…,v0N]⊤. We obtain the global existence and uniqueness of a solution provided that (E0h,v0h)(E0h,v0h) are sufficiently small in (Ḃ2,1N2−1∩Ḃ2,1N2)×Ḃ2,1N2−1, while E0NE0N and v0Nv0N are large, where E0h=[E0,ij](N−1)×NE0h=[E0,ij](N−1)×N, v0h=[v01,…,v0,N−1]⊤v0h=[v01,…,v0,N−1]⊤ and E0N=[E0,N1,…,E0,NN]E0N=[E0,N1,…,E0,NN].