Zobrazeno 1 - 10
of 144
pro vyhledávání: '"Zlatos, Andrej"'
Autor:
Zlatos, Andrej
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock). Existence of
Externí odkaz:
http://arxiv.org/abs/2401.14660
Autor:
Zlatos, Andrej
We prove local well-posedness for the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g.
Externí odkaz:
http://arxiv.org/abs/2401.14659
Autor:
Zlatos, Andrej
We show that the generalized SQG equation with $\alpha\in(0,\frac 14]$ is locally well-posed on the half-plane in spaces of bounded integrable solutions that are natural for its dynamic on domains with boundaries, and allow for some power growth of t
Externí odkaz:
http://arxiv.org/abs/2305.02427
Autor:
Han, Zonglin, Zlatos, Andrej
We show that particle trajectories for positive vorticity solutions to the 2D Euler equations on fairly general bounded simply connected domains cannot reach the boundary in finite time. This includes domains with possibly nowhere $C^1$ boundaries an
Externí odkaz:
http://arxiv.org/abs/2206.01405
Autor:
Zlatos, Andrej
We prove homogenization for reaction-advection-diffusion equations with KPP reactions, in the time-periodic spatially stationary ergodic setting, and find an explicit formula for the homogenized dynamic. We also extend this result to models with non-
Externí odkaz:
http://arxiv.org/abs/2203.15962
Autor:
Zhang, Yuming Paul, Zlatos, Andrej
We prove stochastic homogenization for reaction-advection-diffusion equations with random space-time-dependent KPP reactions with temporal correlations that are decaying in an appropriate sense. We show that the limiting homogenized dynamic has the s
Externí odkaz:
http://arxiv.org/abs/2202.08254
Autor:
Zhang, Yuming Paul, Zlatos, Andrej
We prove time-dependent versions of Kingman's subadditive ergodic theorem, which can be used to study stochastic processes as well as propagation of solutions to PDE in time-dependent environments.
Comment: 24 pages
Comment: 24 pages
Externí odkaz:
http://arxiv.org/abs/2202.07783
Autor:
Zlatos, Andrej
We show that long time solution dynamic for general reaction-advection-diffusion equations with KPP reactions is virtually linear in the following sense. Its leading order depends on the non-linear reaction only through its linearization at $u=0$, an
Externí odkaz:
http://arxiv.org/abs/2202.07743
Autor:
Jeon, Junekey, Zlatoš, Andrej
Publikováno v:
Analysis & PDE 17 (2024) 1005-1018
We prove that splash-like singularities cannot occur for sufficiently regular patch solutions to the generalized surface quasi-geostrophic equation on the plane or half-plane with parameter $\alpha\le \frac 14$. This includes potential touches of mor
Externí odkaz:
http://arxiv.org/abs/2112.00191