| Abstract: |
| In this talk, we are concerned with 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 $\mathbb{R}^3$ and derive decay estimates for the solution and its spatial derivatives in $L^p$ norms for all $p \ge 1$. The analysis is based on a Green`s function approach for the associated variable-coefficient linearized operator.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. This talk is based on recent joint work with Professor Yoshiyuki Kagei |
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