57 citations · 221 across the 19 of their papers we have counts for
19 papers
Nodal lengths of eigenfunctions in the disc
Xiaolong Han, Michael Murray, Chuong Tran
In this paper, we derive the sharp lower and upper bounds of nodal lengths of Laplacian eigenfunctions in the disc. Furthermore, we observe a geometric property of the eigenfunctio…
Note on Solution Regularity of the Generalized Magnetohydrodynamic Equations with Partial Dissipation
Chuong V. Tran, Xinwei Yu, Zhichun Zhai
In this brief note we study the -dimensional magnetohydrodynamic equations with hyper-viscosity and zero resistivity. We prove global regularity of solutions when the hyper-visc…
On Global Regularity of 2D Generalized Magnetohydrodynamic Equations
Chuong V. Tran, Xinwei Yu, Zhichun Zhai
In this article we study the global regularity of 2D generalized magnetohydrodynamic equations (2D GMHD), in which the dissipation terms are and $- κ(-\trian…
Energy dissipation and resolution of steep gradients in one-dimensional Burgers flows
Chuong V. Tran, David G. Dritschel
Travelling-wave solutions of the inviscid Burgers equation having smooth initial wave profiles of suitable shapes are known to develop shocks (infinite gradients) in finite times.…
Effective degrees of nonlinearity in a family of generalized models of two-dimensional turbulence
Chuong V. Tran, David G. Dritschel, Richard K. Scott
We study the small-scale behavior of generalized two-dimensional turbulence governed by a family of model equations, in which the active scalar is advected by the i…
The number of degrees of freedom of three-dimensional Navier--Stokes turbulence
Chuong V. Tran
In Kolmogorov's phenomenological theory of turbulence, the energy spectrum in the inertial range scales with the wave number as and extends up to a dissipation wave…