6 papers
A priori error estimates for the -method for the flow of nonsmooth velocity fields
Gennaro Ciampa, Tommaso Cortopassi, Gianluca Crippa +2
Velocity fields with low regularity (below the Lipschitz threshold) naturally arise in many models from mathematical physics, such as the inhomogeneous incompressible Navier-Stokes…
A generalised Nehari manifold method for a class of non linear Schrödinger systems in
Tommaso Cortopassi, Vladimir Georgiev
We study the existence of positive solutions of a particular elliptic system in composed of two coupled non linear stationary Schrödinger equations (NLSEs), that is…
A current based approach for the uniqueness of the continuity equation
Tommaso Cortopassi
We consider the problem of proving uniqueness of the solution of the continuity equation with a vector field $u \in [L^1 (0,T; W^{1,p}(\mathbb{T}^d)) \cap L^\infty ((0,T) \times \m…
An explicit Euler method for Sobolev vector fields with applications to the continuity equation on non cartesian grids
Tommaso Cortopassi
We prove a novel stability estimate in between the regular Lagrangian flow of a Sobolev vector field and a piecewise affine approximation of such flow. This…
A note on a stability estimate for regular Lagrangian flows
Tommaso Cortopassi
In this note, we prove a version of the well known stability estimate for regular Lagrangian flows derived by Gianluca Crippa and Camillo De Lellis in \cite{crippa2008estimat…
Existence, uniqueness and regularity of the gradient flow of the Ambrosio-Tortorelli functional
Tommaso Cortopassi
We consider the gradient flow of the Ambrosio-Tortorelli functional at fixed , proving existence, uniqueness and $L^2 _t (H_x ^2) \cap L^\infty _t (H^1 _x) \cap H^1 _t (L^2 _x…