Regularity Theory for Nonlinear Partial Differential Equations

非线性偏微分方程的正则性理论项目摘要Vladimir Sverak本项目将研究现代连续介质力学中重要的偏微分方程的数学问题。这些包括Navier-Stokes方程（描述流体流动）和用于非线性弹性和材料科学中的能量泛函的Euler-Lagrange方程（描述材料的变形）。另一个主题是关于控制理论和抛物型方程解的向后唯一性。上述方程在许多应用中是核心，但即使使用功能强大的计算机，也往往很难求解。这与数学理论中尚未解决的问题有关。该项目将解决其中一些问题，其结果可能 对于不同的应用领域具有重要的影响。

Regularity Theory for Nonlinear Partial Differential EquationsProject AbstractVladimir SverakThis project will study mathematical problems for important partial differential equations of modern continuum mechanics. These include the Navier-Stokes equations (which describe fluid flows) and Euler-Lagrange equations for energy functionals used in non-linear elasticity and materials science (which describe deformation of materials). Another topic concerns control theory and backward uniqueness of solutions of parabolic equations.The above equations are central in many applications, but can often be very hard to solve, even with the use of powerful computers. This is related to unresolved problems in the mathematical theory. This project will tackle some of these problems and the results may have important consequences for diverse application areas.