PrerequisiteKnowledges on mathematical physics equations, deep neural networks and the Python language.AbstractDifferential equations can describe various natural and social phenomena. The physics-informed neural networks (PINNs), as a deep learning framework, is a powerful and effective way in solving forward and inverse problems involving differential equations. The course will review the pub...
AbstractIn this talk, we will review the past developments on the solutions of the compressible Navier-Stokes equations and reveal the three hidden structures which linked the weak solution to the strong one. Based on these observations, we proved the Nash's conjecture in 1958s and establish global exsitence theory for both isentropic and heat-conductive compressible Navier-Stokes equations. Mo...
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