Borel Summation and Applications to PDEs

该项目的重点是进一步发展新的和建设性的技术，以证明非线性偏微分方程的解的存在性，特别强调三维Navier-Stokes系统，并确定其整体和渐近性质。非线性偏微分方程是物理学、化学、生物学和其他科学中广泛问题的基本建模工具。 理解它们的解是解释和预测物理现象的关键工具。该项目为这项科学事业开发了新的途径和方法。

The project focuses on further development of new and constructive techniques for proving existence of solutions to nonlinear partial differential equations, with special emphasis on the three-dimensional Navier-Stokes system, and determining their global and asymptotic properties. The methods are based on recent advances in Borel-Laplace regularization and summability.Nonlinear partial differential equations are essential modeling tools in a wide range of problems in physics, chemistry, biology and other sciences. Understanding their solutions is a key tool in interpreting and predicting physical phenomena. The project develops a new approach and methods for this scientific enterprise.