论文标题
多维双曲线Jin-Xin系统的扩散放松极限
Diffusive relaxation limit of the multi-dimensional hyperbolic Jin-Xin system
论文作者
论文摘要
我们研究了在多维环境中Jin-Xin系统对粘性保护定律的扩散松弛极限。对于最初的数据是在合适的均匀BESOV规范中恒定状态的小扰动，我们证明了相对于弛豫参数满足均匀估计值的强溶液的全球良好性。然后，我们证明强大的松弛极限是合理的，并表现出该过程的明确收敛率。我们的证明是基于Crin-Barat和Danchin开发的技术的改编，以便能够处理其他低阶非线性项。
We study the diffusive relaxation limit of the Jin-Xin system toward viscous conservation laws in the multi-dimensional setting. For initial data being small perturbations of a constant state in suitable homogeneous Besov norms, we prove the global well-posedness of strong solutions satisfying uniform estimates with respect to the relaxation parameter. Then, we justify the strong relaxation limit and exhibit an explicit convergence rate of the process. Our proof is based on an adaptation of the techniques developed by Crin-Barat and Danchin to be able to deal with additional low-order nonlinear terms.
