6 papers
On well-posedness of a mildly dissipative family of active scalar equations in borderline Sobolev spaces
Anuj Kumar, Vincent R. Martinez
This paper considers a family of active scalar equations which modify the generalized surface quasi-geostrophic (gSQG) equations through its constitutive law and a dissipative pert…
On Turbulent Behavior of the Generalized Surface Quasigeostrophic Equations
Chengzhang Fu, Michael S. Jolly, Anuj Kumar +1
Turbulent behavior of the two-parameter family of generalized surface quasigeostrophic equations is examined both rigorously and numerically. We adapt a cascade mechanism argument…
Energy dissipation near the outflow boundary in the vanishing viscosity limit
Jincheng Yang, Vincent R. Martinez, Anna L. Mazzucato +1
We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow b…
Reconstruction of wide spectrum forcing in transport-diffusion and Navier-Stokes equations
Jochen Bröcker, Giulia Carigi, Tobias Kuna +1
This article considers the problem of reconstructing unknown driving forces based on incomplete knowledge of the system and its state. This is studied in both a linear and nonlinea…
Upper bounds on the dimension of the global attractor of the 2D Navier-Stokes equations on the plane
Aseel Farhat, Anuj Kumar, Vincent R. Martinez
This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the -pl…
Averaging principle for the stochastic primitive equations in the large rotation limit
Quyuan Lin, Rongchang Liu, Vincent R. Martinez
It is known that the unique ergodicity of the viscous primitive equations with additive white-in-time noise remains an open problem. In this work, we demonstrate that, as the rotat…