8 papers
On wellposedness and limiting behavior of generalized SQG equations
Anuj Kumar
We consider the two-dimensional generalized surface quasi-geostrophic equations in , given by \[\partial_t θ+u\cdot \nabla θ=0,\quad u=-\nabla^{\perp}Λ^{β-2}θ,\,β\in…
Existence of weak solutions to the generalized SQG equations in Sobolev spaces
Anuj Kumar
We consider the two-dimensional dissipative generalized surface quasi-geostrophic equations given by \[\partial_t θ+u\cdot \nabla θ+ν(-Δ)^αθ=0,\quad u=\nabla^{\perp}Λ^{β-2}θ\] and…
Inviscid and fast rotation limit for dispersive generalized SQG equations
Anuj Kumar, Sweety, Mohit Yadav
We consider the dissipative generalized surface quasi-geostrophic equations with a dispersive forcing term and study the behavior of solutions in the limit of vanishing viscosity.…
Asymptotic study of supercritical generalized SQG equations in critical Sobolev spaces
Anuj Kumar
We study the long time behavior of regular solutions of the supercritical gSQG equations in the fully nonlinear regime. More precisely, under the assumption of small initial data i…
Mixing and Small-Scale Formation in a Passive Divergence-Free Vector Field
Anuj Kumar, Franziska Weber
We study mixing for a divergence-free passive vector field transported by another divergence-free vector field , where evolves according to $ \partial_t u + (U \cdot \na…
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…
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 -pla…
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…