Zobrazeno 1 - 10
of 220
pro vyhledávání: '"Crippa, Gianluca"'
We establish local-in-time existence and uniqueness results for nonlocal conservation laws in several space dimensions under weak (that is, Sobolev or BV) differentiability assumptions on the convolution kernel. In contrast to the case of a smooth ke
Externí odkaz:
http://arxiv.org/abs/2408.02423
In this work, we study several properties of the normal Lebesgue trace of vector fields introduced by the second and third author in [18] in the context of the energy conservation for the Euler equations in Onsager-critical classes. Among several pro
Externí odkaz:
http://arxiv.org/abs/2405.11486
The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with $L^p$ initial vorti
Externí odkaz:
http://arxiv.org/abs/2402.07622
Consider a non-local (i.e., involving a convolution term) conservation law: when the convolution term converges to a Dirac delta, in the limit we formally recover a classical (or "local") conservation law. In this note we overview recent progress on
Externí odkaz:
http://arxiv.org/abs/2311.14528
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a unified treatment of the available literature along with some extensions
Externí odkaz:
http://arxiv.org/abs/2310.12625
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced dissipation
Externí odkaz:
http://arxiv.org/abs/2308.00358
Publikováno v:
J. Evol. Equ. 24(1), 1 (2024)
We study the Cauchy problem for the advection-diffusion equation $\partial_t u + \mathrm{div} (u b ) = \Delta u$ associated with a merely integrable divergence-free vector field $b$ defined on the torus. We discuss existence, regularity and uniquenes
Externí odkaz:
http://arxiv.org/abs/2306.15529
In this paper, we study the convergence of solutions of the $\alpha$-Euler equations to solutions of the Euler equations on the $2$-dimensional torus. In particular, given an initial vorticity $\omega_0$ in $L^p_x$ for $p \in (1,\infty)$, we prove st
Externí odkaz:
http://arxiv.org/abs/2306.06641
Existence and stability of weak solutions of the Vlasov--Poisson system in localized Yudovich spaces
We consider the Vlasov--Poisson system both in the repulsive (electrostatic potential) and in the attractive (gravitational potential) cases. In our first main theorem, we prove the uniqueness and the quantitative stability of Lagrangian solutions $f
Externí odkaz:
http://arxiv.org/abs/2306.00523
Autor:
Coclite, Giuseppe Maria, Colombo, Maria, Crippa, Gianluca, De Nitti, Nicola, Keimer, Alexander, Marconi, Elio, Pflug, Lukas, Spinolo, Laura V.
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast \rho$ satisfy an Ole\u{\i}nik-type entropy condition. More precisely,
Externí odkaz:
http://arxiv.org/abs/2304.01309