Published/ Submitted Works:
M.S. Jolly, A. Kumar, and V.R. Martinez, On existence, uniqueness, and smoothing to the generalized SQG equation in critical Sobolev spaces, Communications in Mathematical Physics, 387, 551–596 (2021).
M.S. Jolly, A. Kumar, and V.R. Martinez, On local well-posedness of logarithmic inviscid regularizations of generalized SQG equations in borderline Sobolev spaces, Communications on Pure and Applied Analysis, 21(1): 101-120 (2022) .
A. Kumar and V.R. Martinez, On well-posedness of a mildly dissipative family of active scalar equations in borderline Sobolev spaces, Journal of Differential Equations, Vol 457, 2026
A. Kumar and W. Ozanski, A simple proof of linear instability of shear flows with application to vortex sheets, Journal of Mathematical Fluid Mechanics 27, 34 (2025).
A. Farhat, A. Kumar, and V.R. Martinez, Upper bounds on the dimension of the global attractor of the 2D Navier-Stokes equations on the $\beta$-plane, Nonlinear Analysis, 256, (2025).
A. Kumar and A. Pakzad. Statistical Estimates for 2D stochastic Navier-Stokes Equations, Journal of Statistical Physics (2025).
C. Fu, M. S. Jolly, A. Kumar and V. Martinez. On Turbulent Behavior of the Generalized Surface Quasi-geostrophic Equations. https://arxiv.org/abs/2510.15077 (submitted).