Tommaso Cortopassi

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math.AP2025

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 $L_{t}^{\infty} (L_{x}^{p})$ between the regular Lagrangian flow of a Sobolev vector field and a piecewise affine approximation of such flow. This…

math.AP2025

A priori error estimates for the $I^¸$ -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…

math.AP2024

Existence, uniqueness and $L_{t}^{2} (H_{x}^{2}) \cap L_{t}^{\infty} (H_{x}^{1}) \cap H_{t}^{1} (L_{x}^{2})$ regularity of the gradient flow of the Ambrosio-Tortorelli functional

Tommaso Cortopassi

We consider the gradient flow of the Ambrosio-Tortorelli functional at fixed $I^µ > 0$ , proving existence, uniqueness and $L^2 _t (H_x ^2) \cap L^\infty _t (H^1 _x) \cap H^1 _t (L^2 _…

An explicit Euler method for Sobolev vector fields with applications to the continuity equation on non cartesian grids

A priori error estimates for the I^¸-method for the flow of nonsmooth velocity fields

Existence, uniqueness and Lt2​(Hx2​)∩Lt∞​(Hx1​)∩Ht1​(Lx2​) regularity of the gradient flow of the Ambrosio-Tortorelli functional

A priori error estimates for the $I^¸$ -method for the flow of nonsmooth velocity fields

Existence, uniqueness and $L_{t}^{2} (H_{x}^{2}) \cap L_{t}^{\infty} (H_{x}^{1}) \cap H_{t}^{1} (L_{x}^{2})$ regularity of the gradient flow of the Ambrosio-Tortorelli functional