Vectorial variational problems in L 8 constrained by the Navier-Stokes equations*
Vectorial variational problems in L 8 constrained by the Navier-Stokes equations*
复制标题
受纳维-斯托克斯方程约束的 L 8 向量变分问题*
DOI：
10.1088/1361-6544/ac372a
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发表时间：
2021
期刊：
影响因子：
1.7
通讯作者：
Clark E
中科院分区：
文献类型：
--
作者：
Clark E
本文研究了一类在Lp和L∞中的极小化问题，其中容许映射类受Navier-Stokes方程的约束.这种类型的问题是由气象预报中产生的大气流动的变分数据同化引起的。在这里我们建立了对所有p的PDE约束极小解的存在性，并且当p→∞时，Lp极小解收敛到L∞极小解。我们进一步表明，L p极小解决了欧拉-拉格朗日系统。最后，通过Lp极小化器的逼近构造了所有特殊的L∞极小化器，并将其用于求解一个含测度系数的发散偏微分方程组，该方程组是相应的无发散Aronsson-Euler方程组的一个发散形式的对应方程.
We study a minimisation problem in L p and L∞ for certain cost functionals, where the class of admissible mappings is constrained by the Navier–Stokes equations. Problems of this type are motivated by variational data assimilation for atmospheric flows arising in weather forecasting. Herein we establish the existence of PDE-constrained minimisers for all p, and also that L p minimisers converge to L∞ minimisers as p→∞. We further show that L p minimisers solve an Euler–Lagrange system. Finally, all special L∞ minimisers constructed via approximation by L p minimisers are shown to solve a divergence PDE system involving measure coefficients, which is a divergence-form counterpart of the corresponding non-divergence Aronsson–Euler system.