The initial-boundary value problem for the compressible viscoelastic flows. (English) Zbl 1304.35548
Summary: The initial-boundary value problem for the equations of compressible viscoelastic flows is considered in a bounded domain of three-dimensional spatial dimensions. The global existence of strong solution near equilibrium is established. Uniform estimates in \(W^{1,q}\) with \(q>3\) on the density and deformation gradient are also obtained.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76A10 | Viscoelastic fluids |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 35D35 | Strong solutions to PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35B30 | Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs |
Keywords:
compressible viscoelastic flows; initial-boundary value problem; strong solution; existenceReferences:
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