Global existence of strong solutions for the equations of non-isentropic incompressible viscoelastic fluids with large data

This paper investigates the global strong solutions of non-isentropic incompressible viscoelastic fluids in the periodic domain. When the initial velocity, deformation and temperature is small for the given physical parameters, we prove that the global existence and uniquence of strong solutions. And the result mathematically verifies that for the large elasticity coefficient, the initial velocity and temperature can be large. Moreover, we also get decay-in-time estimates and find that the velocity decays (exponential decay) faster than the temperature (algebraic decay) in Lagrangian coordinates.