In this paper we investigate a non-linear and non-local one dimensional transport equation
under random perturbations on the real line. We first establish a local-in-time theory, ie …

We analyze finite-time blowup scenarios of locally self-similar type for the inviscid
generalized surface quasi-geostrophic equation (gSQG) in R 2. Under an L r growth …

This paper studies the dissipative generalized surface quasi-geostrophic equations in a
supercritical regime where the order of the dissipation is small relative to order of the …

We construct various statistical ensembles associated to the 3D Euler equations and prove
global regularity of these equations for data living on these sets. Similar results are also …

This paper is concerned with the global well-posedness of the two-dimensional
incompressible vorticity equation in the half plane. Under the assumption that the initial …

In this paper, we present a new and elementary proof of the local existence and uniqueness
of the classical solution to the Cauchy problem of the two-dimensional generalized surface …

In this paper we consider the hyperelastic rod equation on the Sobolev spaces H^ s (R) H s
(R), s> 3/2 s> 3/2. Using a geometric approach we show that for any T> 0 T> 0 the …

In this paper, we consider the incompressible porous media equation on the Sobolev space
H s (R 2), s> 2. We provide a Lagrangian formulation of this equation on the Sobolev-type …

In this paper we investigate a non-linear and non-local one dimensional transport equation
under random perturbations on the real line. We first establish a local-in-time theory, ie …

In this paper, we consider the inviscid 2D Boussinesq equation on the Sobolev spaces H^ s
(\mathbb R^ 2) H s (R 2), s> 2 s> 2. Using a geometric approach, we show that for any T> 0 …