An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918322890604544 |
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| author | Lasser, Caroline Lunowa, Stephan B. Wohlmuth, Barbara |
| author_facet | Lasser, Caroline Lunowa, Stephan B. Wohlmuth, Barbara |
| contents | We establish rigorously the equivalence between classical moment closure and a nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow in the linearized Hookean spring chain setting. The variational formulation is based on the Dirac-Frankel principle applied to a Gaussian approximation manifold endowed with the Fisher-Rao information metric. We show that the invariance of this manifold under the linear configurational dynamics yields an exact evolution for the macroscopic conformation tensor, recovering the classical diffusive Oldroyd-B closure. While the equivalence only holds in the linearized setting, the associated variational framework provides an abstract error representation and a starting point for the systematic construction of reduced approximation schemes for polymeric flows with nonlinear forcing laws. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_04644 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow Lasser, Caroline Lunowa, Stephan B. Wohlmuth, Barbara Spectral Theory Mathematical Physics 37L65, 58E30, 35Q84, 76D05 We establish rigorously the equivalence between classical moment closure and a nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow in the linearized Hookean spring chain setting. The variational formulation is based on the Dirac-Frankel principle applied to a Gaussian approximation manifold endowed with the Fisher-Rao information metric. We show that the invariance of this manifold under the linear configurational dynamics yields an exact evolution for the macroscopic conformation tensor, recovering the classical diffusive Oldroyd-B closure. While the equivalence only holds in the linearized setting, the associated variational framework provides an abstract error representation and a starting point for the systematic construction of reduced approximation schemes for polymeric flows with nonlinear forcing laws. |
| title | An equivalence of moment closure and nonlinear variational approximation of the Fokker-Planck equation for dilute polymeric flow |
| topic | Spectral Theory Mathematical Physics 37L65, 58E30, 35Q84, 76D05 |
| url | https://arxiv.org/abs/2602.04644 |