Global existence and well-posedness for the Doi-Edwards polymer model
| Autor: | Zhaoyang Yin, Wei Luo |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Cauchy stress tensor
Applied Mathematics Mathematical analysis Degenerate energy levels Mathematics::Analysis of PDEs Function (mathematics) Condensed Matter::Soft Condensed Matter Dimension (vector space) Finite strain theory Initial value problem Tensor Convection–diffusion equation Analysis Mathematics |
| Zdroj: | Journal of Differential Equations. 309:142-175 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2021.10.064 |
| Popis: | In this paper we mainly investigate the Cauchy problem of the Doi-Edwards polymer model with dimension d ≥ 2 . The model was derived in the late 1970s to describe the dynamics of polymers in melts. The system contains a Navier-Stokes equation with an additional stress tensor which depend on the deformation gradient tensor and the memory function. The deformation gradient tensor satisfies a transport equation and the memory function satisfies a degenerate parabolic equation. We first proved the local well-posedness for the Doi-Edwards polymer model in Besov spaces by using the Littlewood-Paley theory. Moreover, if the initial velocity and the initial memory is small enough, we obtain a global existence result. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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