11 citations · 22 across the 18 of their papers we have counts for
21 papers
A Liouville theorem for the two-dimensional stationary hypodissipative Navier--Stokes system
Nicola De Nitti, Lukas Niebel, Jiaqi Yang
We study the two-dimensional stationary incompressible Navier--Stokes equations on with fractional dissipation . In the full range , we prove tha…
Superharmonicity of the fractional ground state
Nicola De Nitti, Xavier Fernández-Real, Florian Grube +1
We prove that the positive ground state of the fractional Laplacian , , on an arbitrary open set satisfies in . In one dimension,…
Stability and instability of a one-dimensional MHD model
Nicola De Nitti, Jie Guo, Quansen Jiu
We consider a one-dimensional magnetohydrodynamics model introduced by Dai \textit{et al.}~(2023), in a parameter regime where, in the absence of a magnetic field, the system reduc…
Controllability of a One-Dimensional Dynamic Debonding Model
Nicola De Nitti, Arick Shao
We investigate a one-dimensional dynamic debonding model, introduced by Freund (1990), in which the wave equation is coupled with a Griffith criterion governing the propagation of…
Regularity aspects of Leray-Hopf solutions to the 2D Inhomogeneous Navier-Stokes system and applications to weak-strong uniqueness
Timothée Crin-Barat, Nicola De Nitti, Stefan Škondrić +1
We characterize the Leray--Hopf solutions of the 2D inhomogeneous Navier--Stokes system that become strong for positive times. This characterization relies on the strong energy ine…
Fractional cross-diffusion in a bounded domain: existence, weak-strong uniqueness, and long-time asymptotics
Nicola De Nitti, Nicola Zamponi
We study a fractional cross-diffusion system that describes the evolution of multi-species populations in the regime of large-distance interactions in a bounded domain. We prove ex…
Nested discontinuous asymptotic profiles for the viscous Burgers equation with infinite mass
Nicola de Nitti, Eliot Pacherie
We study the viscous Burgers equation with a family of initial data having infinite mass. After rescaling, the solution converges toward a bounded discontinuous profile in the long…
Existence and finite speed of propagation of solutions for a multi-dimensional fractional thin-film equation
Nicola De Nitti, Stefano Lisini, Antonio Segatti +1
In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bound…
Optimal Regularity for the 2D Euler Equations in the Yudovich class
Nicola de Nitti, David Meyer, Christian Seis
We analyze the optimal regularity that is exactly propagated by a transport equation driven by a velocity field with BMO gradient. As an application, we study the 2D Euler equation…
Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings
Giuseppe Maria Coclite, Nicola De Nitti, Francesco Maddalena +2
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body…
Sharp bounds on enstrophy growth for viscous scalar conservation laws
Dallas Albritton, Nicola De Nitti
We prove sharp bounds on the enstrophy growth in viscous scalar conservation laws. The upper bound is, up to a prefactor, the enstrophy created by the steepest viscous shock admiss…
Symmetry results for some overdetermined obstacle problems
Nicola De Nitti, Shigeru Sakaguchi
We establish symmetry results for two categories of overdetermined obstacle problems: a Serrin-type problem and a two-phase problem under the overdetermination that the interface s…
Fractional Hardy-Rellich inequalities via integration by parts
Nicola De Nitti, Sidy Moctar Djitte
We prove a fractional Hardy-Rellich inequality with an explicit constant in bounded domains of class . The strategy of the proof generalizes an approach pioneered by E. Mi…
Ole\uınik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit
Giuseppe Maria Coclite, Maria Colombo, Gianluca Crippa +5
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast…
Scaling limits for fractional polyharmonic Gaussian fields
Nicola De Nitti, Florian Schweiger
This work is concerned with fractional Gaussian fields, i.e. Gaussian fields whose covariance operator is given by the inverse fractional Laplacian (where, in particula…
The stationary critical points of the fractional heat flow
Nicola De Nitti, Shigeru Sakaguchi
We study the spatial critical points of the solutions of the fractional heat equation. For the Cauchy problem, we show that the origin satisfies $\nabla_x u(0,t) = 0…
Stability with explicit constants of the critical points of the fractional Sobolev inequality and applications to fast diffusion
Nicola De Nitti, Tobias König
We study the quantitative stability of critical points of the fractional Sobolev inequality. We show that, for a non-negative function whose energy sa…
On the decay of one-dimensional locally and partially dissipated hyperbolic systems
Timothée Crin-Barat, Nicola De Nitti, Enrique Zuazua
We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the cl…
On Liouville-type theorems for the 2D stationary MHD equations
Nicola De Nitti, Francis Hounkpe, Simon Schulz
We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Di…
A general result on the approximation of local conservation laws by nonlocal conservation laws: The singular limit problem for exponential kernels
Giuseppe Maria Coclite, Jean-Michel Coron, Nicola De Nitti +2
We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential…
Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation
Nicola De Nitti, Julian Fischer
We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distrib…