Regularity Theory for Nonlinear Partial Differential Equations

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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.