分数正则化反卷积磁流体动力学模型的全局适定性
Global well-posedness for Deconvolution Magnetohydrodynamics models with Fractional regularization
摘要：
本文考虑了与大涡模拟有关的两种近似反卷积磁流体动力学模型。我们首先研究了双粘性情形下解的存在唯一性。然后，我们研究了具有磁扩散系数但不具有运动粘性的近似反卷积MHD模型解的存在唯一性。在每种情况下，我们给出了正则化的最优值，我们可以证明整体存在性和唯一性的解决方案。第二模型包括近似反卷积欧拉模型作为特定情况。最后，在正则化参数条件较弱的情况下，证明了双粘性系统的渐近稳定性。
英文摘要：
In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics models which are related to Large Eddy Simulation. We first study existence and uniqueness of solutions in the double viscous case. Then, we study existence and uniqueness of solutions of the Approximate Deconvolution MHD model with magnetic diffusivity, but without kinematic viscosity. In each case, we give the optimal value of regularizations where we can prove global existence and uniqueness of the solutions. The second model includes the Approximate Deconvolution Euler Model as a particular case. Finally, an asymptotic stability result is shown in the double viscous case with weaker condition on the regularization parameter.
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