This paper studies a family of generalized surface quasi-geostrophic (SQG) equations for an
active scalar $\theta $ on the whole plane whose velocities have been mildly regularized, for …

In this paper, we are concerned with the long-time asymptotic behavior of the generalized
two-dimensional quasi-geostrophic equation. More precisely, we obtain the sharp time …

Motivated by the possibility of noise to cure equations of finite-time blowup, the recent work
by the second and third named authors showed that with quantifiable high probability …

We study a family of active scalar equations which interpolate between the 2D
incompressible Euler equations and the (inviscid) surface quasi-geostrophic equation. We …

We consider the two dimensional surface quasi-geostrophic equations with super-critical
dissipation. For large initial data in critical Sobolev and Besov spaces, we prove optimal …

This paper considers a family of active scalar equations which modify the generalized
surface quasi-geostrophic (gSQG) equations through its constitutive law or dissipative …

Our interest in this research is to prove the decay, as time tends to infinity, of a unique global
solution for the supercritical case of the modified quasi-gesotrophic equation (MQG) θ t+(-Δ) …

This paper considers the dynamics of the forced critical modified surface quasi-geostrophic
equation on T 2 as the index α of the dissipative operator Λ α belongs to [1, 2). At first, when …

The generalized surface quasi-geostrophic equations (gSQG) is a family of active scalar
transport equations that interpolates between the 2D incompressible Euler equation and the …

Well-posedness of the Cauchy initial value problem (IVP) is a fundamental issue in the study
of evolutionary equations as it asserts the existence and uniqueness of solutions, as well as …