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math.AP2025
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…
math.AP2025
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…
math.AP2025
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…