Global strong solution for the density dependent incompressible viscoelastic fluids in the critical Lp framework

In this paper, we consider the Cauchy problem of the density dependent incompressible viscoelastic fluids in the whole space Rd(d≥2) with the initial data close to a stable equilibrium. This work is dedicated to deriving the existence result of the global strong solution in the critical space with respect to the natural scaling of the equations in the Lp framework.