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math.NA2025
Error estimates of physics-informed neural networks for approximating Boltzmann equation
Elie Abdo, Lihui Chai, Ruimeng Hu +1
Motivated by the recent successful application of physics-informed neural networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu, J. Sci. Comput., 94 (2023),…
math.AP2025
Well-posedness and ill-posedness of the primitive equations with fractional horizontal dissipation
Elie Abdo, Quyuan Lin, Changhui Tan
The primitive equations (PE) are a fundamental model in geophysical fluid dynamics. While the viscous PE are globally well-posed, their inviscid counterparts are known to be ill-po…
math.AP2025
Electroconvection in a Magnetic Field
Elie Abdo, Peter Constantin, Mihaela Ignatova +1
Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak soluti…