Global well-posedness and incompressible limit of two-dimensional generalized compressible Oldroyd-B system with large velocity

The global-in-time strong solutions to two-dimensional generalized compressible Oldroyd-B viscoelastic equations with large velocity on the torus are derived via the incompressible limit. For a given positive shear viscosity and a given initial velocity of large size, the solutions are global-in-time and are driven toward incompressibility when the bulk viscosity coefficient is large enough and the initial density is close to a certain positive constant. The main ingredient is that the fluid velocity is decomposed into the divergence-free part and the potential part to carry out the weighted energy estimations, respectively. Compared with the previous work in 3D case, we have improved the techniques, including the use of the Ladyzhenskaya inequality, to obtain the smallness of the density variation. In addition, the modified techniques are applicable to both 2D and 3D cases.