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math.AP2024
The Muskat problem with a large slope
Yiran Xu, Stephen Cameron, Ke Chen +2
In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity \(β_σ(f_0'…
math.AP2024
Well-posedness for local and nonlocal quasilinear evolution equations in fluids and geometry
Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
We establish a Schauder-type estimate for general local and non-local linear parabolic system in where $Λ=(-Δ)^{…