Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Rosati, Tommaso"'
We consider the top Lyapunov exponent associated to the advection-diffusion and linearised Navier-Stokes equations on the two-dimensional torus. The velocity field is given by the stochastic Navier-Stokes equations driven by a non-degenerate white-in
Externí odkaz:
http://arxiv.org/abs/2411.10419
Autor:
Blessing, Alexandra, Rosati, Tommaso
This work studies the instability of stochastic scalar reaction diffusion equations, driven by a multiplicative noise that is white in time and smooth in space, near to zero, which is assumed to be a fixed point for the equation. We prove that if the
Externí odkaz:
http://arxiv.org/abs/2406.04651
This work considers the two-dimensional Allen-Cahn equation $$ \partial_t u = \frac{1}{2}\Delta u + \mathfrak{m}\, u -u^3\;, \quad u(0,x)= \eta (x)\;, \qquad \forall (t,x) \in [0, \infty) \times \mathbb{R}^{2} \;, $$ where the initial condition $ \et
Externí odkaz:
http://arxiv.org/abs/2311.04628
Autor:
Hairer, Martin, Rosati, Tommaso
This work studies the angular component $ \pi_{t} = u_{t} / \| u_{t} \| $ associated to the solution $ u $ of a vector-valued linear hyperviscous SPDE on a $d$-dimensional torus $$\mathrm{d} u^{\alpha} =- \nu^{\alpha} (- \Delta)^{\mathbf{a} } u^{\alp
Externí odkaz:
http://arxiv.org/abs/2307.07472
Autor:
Hairer, Martin, Rosati, Tommaso
We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations \begin{equation*} \partial_t u + u \cdot \nabla u = \Delta u - \nabla p + \zeta + \xi \;, \quad u (0, \cdot) = u_{0}(\cdot) \;, \quad \mathrm{div} (
Externí odkaz:
http://arxiv.org/abs/2301.11059
Autor:
Djurdjevac, Ana, Rosati, Tommaso
We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not rely on a strict maximum principle, and builds instead on a quantitat
Externí odkaz:
http://arxiv.org/abs/2211.05814
We consider the Allen-Cahn equation $\partial_t u- \Delta u=u-u^3$ with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described
Externí odkaz:
http://arxiv.org/abs/2201.08426
Autor:
Rosati, Tommaso, Tóbiás, András
We consider a Fisher-KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed $ \mathfrak{s}> 0 $ given by $\frac{\mathfrak{s}^{2}}{2} = \int_{[0, 1]}\frac{ \log{(1 + y)}}{y} \mat
Externí odkaz:
http://arxiv.org/abs/2201.08196
Autor:
Rosati, Tommaso
Motivated by the evolution of a population in a slowly varying random environment, we consider the 1D Anderson model on finite volume, with viscosity $ \kappa > 0 $: $$ \partial_{t} u(t,x) = \kappa \Delta u(t,x) + \xi(t, x) u(t,x), \quad u(0, x) = u_
Externí odkaz:
http://arxiv.org/abs/2109.14698
