Unconditional finite amplitude stability of a viscoelastic fluid in a mechanically isolated vessel with spatially non-uniform wall temperature

We investigate finite amplitude stability of spatially inhomogeneous steady state an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at non-uniform temperature. For wide class models including the Oldroyd-B model, Giesekus FENE-P Johnson–Segalman and Phan–Thien–Tanner model we prove that is stable subject to any perturbation.