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We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
We use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted So...
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high ord...
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
We consider the semiclassical limit from the Hartree equation with Coulomb interaction potential to the Vlasov–Poisson equation. Using a new stability estimate for the difference of the square roots o...
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as the finite el...
In this talk, we consider a class of exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard equation. We first use the Fourier collocation method to discretize the space do...

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