Regular flows of weakly compressible viscoelastic fluids and the incompressible limit

Strong solutions of 3D compressible Oldroyd‐B fluids

“…Following the ideas of Cho, Choe, and Kim [21,22] in the study of Navier-Stokes equations, we establish the existence and uniqueness of local strong solutions to (7). The initial data 0 and 0 here are of slightly lower regularities compared with that in [1] and [18]. Moreover, we give a blow-up criterion for the strong solution obtained earlier.…”

“…η s = ημ ∕ λ and ξ s are the solvent viscosity and the group viscosity, respectively. In this paper, following Guillopé, Salloum, and Talhouk , we assume that ξ s = 0. Using , we deduce from 3 that τ e satisfies where η e = η − η s is the polymer viscosity.…”

Global existence of classical solutions for the 3D generalized compressible Oldroyd‐B model

“…Lei and Guillope et al investigated the incompressible limit problem in torus and bounded domain, respectively. The ill‐prepared initial data theorem was studied by Fang and Zi .…”

Existence of large-data finite-energy global weak solutions to a compressible Oldroyd-B model

“…Lei [33] proved the local and global existence of classical solutions to a compressible Oldroyd-B system in a torus with small initial data; he also studied the incompressible limit problem and showed that solutions to the compressible flow model with well-prepared initial data converge to those of the incompressible model when the Mach number converges to zero. Guillopé, Salloum, and Talhouk [25] investigated weakly compressible viscoelastic fluids satisfying the Oldroyd constitutive law; they obtained a priori estimates that are uniform in the Mach number, which then allowed them to prove that weakly compressible flows with well-prepared initial data converge to incompressible flows when the Mach number converges to zero. The existence of measure-valued solutions to non-Newtonian compressible, isothermal, monopolar fluid flow models was studied by Nečasová in [40,41]; for bipolar isothermal non-Newtonian compressible fluids related analysis was pursued in [42].…”