论文标题
良好的和良好的多孔道能量的规律性
Well-posedness and Regularity for a Polyconvex Energy
论文作者
论文摘要
我们证明了在两个和三个维度中函数的最小化函数的最小化器的存在，唯一性和规则性，这对应于$ h^1 $投影量的量度保留地图。我们的结果介绍了基于Lagrange乘数的较小性，介绍了有关最小化器独特性的新标准。不需要对第二个衍生物的估计来获得独特的全球最小化器。作为一个应用程序，我们构建了一个最小化的运动方案，以在短时间间隔内构建Navier-Stokes方程的$ l^r $解决方案。
We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional in two and three dimensions, which corresponds to the $H^1$ projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. As an application, we construct a minimizing movement scheme to construct $L^r$ solutions of the Navier-Stokes equation for a short time interval.
