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来证明非线性偏微分方程解的存在性，特别是三维Navier-Stokes系统，并确定其全局和渐近性质。这些方法基于Borel-Laplace正则化和可和性方面的最新进展。非线性偏微分方程组是物理、化学、生物和其他科学中广泛应用的建模工具。理解它们的解决方案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辟了一条新的途径和方法。

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.