Curvilinear Structure Tracking Based on Dynamic Curvature-penalized Geodesics
International audience
Robust prediction interval estimation for Gaussian processes by cross-validation method
International audience
Reachable set for Hamilton–Jacobi equations with non-smooth Hamiltonian and scalar conservation laws
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Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity
We analyze a class of time discretizations for solving the nonlinear Schrödinger equation with non-smooth potential and at low-regularity on an arbitrary Lipschitz domain Ω ⊂ R d , d ≤ 3. We show that these schemes, together with their optimal local error structure, allow for convergence under lower regularity assumptions on both the solution and t...
On the influence of gravity in the dynamics of geophysical flows
In the present paper, we study a multiscale limit for the barotropic Navier-Stokes system with Coriolis and gravitational forces, for vanishing values of the Mach, Rossby and Froude numbers ($\rm Ma$, $\rm Ro$ and $\rm Fr$, respectively). The focus here is on the effects of gravity: albeit remaining in a low stratification regime ${\rm Ma}/{\rm Fr}...
Boundary stabilization of one-dimensional cross-diffusion systems in a moving domain: linearized system
We study the boundary stabilization of one-dimensional cross-diffusion systems in a moving domain. We show first exponential stabilization and then finite-time stabilization in arbitrary small time of the linearized system around uniform equilibria, provided the system has an entropic structure with a symmetric mobility matrix. One example of such ...
On expansions for nonlinear systems, error estimates and convergence issues
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to decouple time-dependent features from geometry-dependent features of the solution have been extensively studied. ...
Fine asymptotic expansion of the ODE's flow
In this paper, we study the asymptotic expansion of the flow X(t, x) solution to the nonlinear ODE: X (t, x) = b X(t, x) with X(0, x) = x ∈ R d , where b is a regular Z dperiodic vector field in R d. More precisely, we provide various conditions on b to obtain a "fine" asymptotic expansion of X of the type: |X(t, x) − x − t ζ(x)| ≤ M
A Linear Stochastic Model of Turbulent Cascades and Fractional Fields
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and the rate of energy dissipation remains bounded from below even if the fluid viscosity tends to zero. A mathem...
An inequality for the solutions to an elliptic equation with weight
We derive a local uniform boundedness result for an equation with weight having interior singularity and log-holder weight. Also we have, sup u = f (inf u).
