Nonlinear Analysis· 2026Q1
Enhanced dissipation and global well-posedness for a three-dimensional flame propagation model with couette flow
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- Q1SCImago
- 2026year
Short summary
Couette flow enhances dissipation in a 3D gravity-induced flame propagation model, proving global well-posedness for the Cauchy problem and deriving decay estimates for solutions and their derivatives.
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Key points
- Couette flow enhances dissipation in a 3D gravity-induced flame propagation model.
- Global-in-time well-posedness of the Cauchy problem in ℝ³ is proven.
- Decay estimates for solutions and their spatial derivatives in Lᵖ norms (p>1) are derived.
- Analysis relies on a Green's function approach, transferring spectral domain decay to physical space.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study a three-dimensional gravity-induced flame front model under a Couette flow. By exploiting the enhanced dissipation induced by the Couette flow, we prove global-in-time well-posedness of the Cauchy problem in ℝ 3 and derive decay estimates for the solution and its spatial derivatives in L p norms for all p > 1. The analysis is based on a Green’s function approach for the associated variable-coefficient linearized operator. Since an explicit representation of the Green’s function is unavailable, we first establish decay estimates in the spectral domain and then transfer them to physical space. These results show that enhanced dissipation induced by the Couette flow is the key mechanism leading to global existence in the whole space, in the large initial data regime.
The authors' abstract, as published at the source. Nonlinear Analysis, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics