论文标题
LP框架中部分耗散双曲线系统的全球存在和放松限制
Global existence for partially dissipative hyperbolic systems in the Lp framework, and relaxation limit
论文作者
论文摘要
在这里，我们研究了在关键均匀besov空间框架内的一类部分耗散双曲线系统的全球强解决方案。我们的主要目的是将对先前论文[10]的分析扩展到一个功能框架，在该功能框架中，该解决方案的低频仅在P大于2的L P型空间中进行界定。这使我们能够为全球良好的较弱条件开出较弱的小型条件，并在构造解决方案的定性特性上获得更准确的信息。我们的存在定理尤其适用于具有松弛的多维等粒子可压缩的Euler系统，并为我们提供独立于放松参数的边界。结果，我们严格地证明了对多孔媒体方程式的放松限制，并表现出适当规范的明确收敛速度，这是我们所知的全新结果。
Here we investigate global strong solutions for a class of partially dissipative hyperbolic systems in the framework of critical homogeneous Besov spaces. Our primary goal is to extend the analysis of our previous paper [10] to a functional framework where the low frequencies of the solution are only bounded in L p-type spaces with p larger than 2. This enables us to prescribe weaker smallness conditions for global well-posedness and to get a more accurate information on the qualitative properties of the constructed solutions. Our existence theorem in particular applies to the multi-dimensional isentropic compressible Euler system with relaxation, and provide us with bounds that are independent of the relaxation parameter. As a consequence, we justify rigorously the relaxation limit to the porous media equation and exhibit explicit rates of convergence for suitable norms, a completely new result to the best of our knowledge.
