arXiv subjects

Weiren Zhao

Publications and source records attributed to Weiren Zhao.

39 records · Page 3Linked to original sources

arXiv2017

Commutator Estimates for the Dirichlet-to-Neumann Map of Stokes Systems in Lipschitz Domains

In the paper, we establish commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's bilinear estimates, and the results may be regarded as an extension of [Dahlberg, Poisson semigroups and singular integrals, Proc. Amer. Math. Soc., 97(1986), no.1, 41-48.] and [Shen, Commutator estimates for the Dirichlet-to-Neumann map in Lipschitz domains, Some topics in harmonic analysis and applications, 369C384, Adv. Lect. Math. (ALM)34, Int. Press, Somerville, MA, 2016.] to Stokes systems.

math.AP↗

arXiv2015

Linear inviscid damping for a class of monotone shear flow in Sobolev spaces

In this paper, we prove the decay estimates of the velocity and $H^1$ scattering for the 2D linearized Euler equations around a class of monotone shear flow in a finite channel. Our result is consistent with the decay rate predicted by Case in 1960.

math.AP↗

arXiv2015

Local well-posedness and break-down criterion of the incompressible Euler equations with free boundary

In this paper, we prove the local well-posedness of the free boundary problem for the incompressible Euler equations in low regularity Sobolev spaces, in which the velocity is a Lipschtiz function and the free surface belongs to $C^{\f32+\varepsilon}$. Moreover, we also present a Beale-Kato-Majda type break-down criterion of smooth solution in terms of the mean curvature of the free surface, the gradient of the velocity and Taylor sign condition.

math.AP↗