21 citations · 21 across the 5 of their papers we have counts for
5 papers
On the rate of convergence of the two-dimensional -models of turbulence to the Navier-Stokes equations
Y. Cao, E. S. Titi
Rates of convergence of solutions of various two-dimensional regularization models, subject to periodic boundary conditions, toward solutions of the exact Navier-Stokes equatio…
Modulation theory for self-focusing in the nonlinear Schrödinger-Helmholtz equation
Yanping Cao, Ziad H. Musslimani, Edriss S. Titi
The nonlinear Schrödinger-Helmholtz (SH) equation in space dimensions with nonlinear power was proposed as a regularization of the classical nonlinear Schrödinger (NLS) eq…
Nonlinear Schrodinger-Helmholtz Equation as Numerical Regularization of the Nonlinear Schrodinger Equation
Yanping Cao, Ziad H. Musslimani, Edriss S. Titi
A regularized system of the Nonlinear Schrödinger Equation (NLS) with nonlinear power in dimension is studied. We prove existence and uniqueness of local solution in t…
Global Well-posedness of the Three-dimensional Viscous and Inviscid Simplified Bardina Turbulence Models
Y. Cao, E. M. Lunasin, E. S. Titi
In this paper we present analytical studies of three-dimensional viscous and inviscid simplified Bardina turbulence models with periodic boundary conditions. The global existence a…
Trivial Stationary Solutions to the Kuramoto-Sivashinsky and Certain Nonlinear Elliptic Equations
Yanping Cao, Edriss S. Titi
We show that the only locally integrable stationary solutions to the integrated Kuramoto-Sivashinsky equation in and are the trivial constant solutions. We extend our tec…