Zobrazeno 1 - 10
of 668
pro vyhledávání: '"Colombo, María"'
Given a divergence-free vector field ${\bf u} \in L^\infty_t W^{1,p}_x(\mathbb R^d)$ and a nonnegative initial datum $\rho_0 \in L^r$, the celebrated DiPerna--Lions theory established the uniqueness of the weak solution in the class of $L^\infty_t L^
Externí odkaz:
http://arxiv.org/abs/2405.01670
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
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
We answer positively to [BDL22, Question 2.4] by building new examples of solutions to the forced 3d-Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissipation and which enjoy uniform bounds in the space $L_t^3 C_x^{1/3 - \
Externí odkaz:
http://arxiv.org/abs/2212.08413
This paper studies the infinite-width limit of deep linear neural networks initialized with random parameters. We obtain that, when the number of neurons diverges, the training dynamics converge (in a precise sense) to the dynamics obtained from a gr
Externí odkaz:
http://arxiv.org/abs/2211.16980
Autor:
Albritton, Dallas, Colombo, Maria
We exhibit non-unique Leray solutions of the forced Navier-Stokes equations with hypodissipation in two dimensions. Unlike the solutions constructed in \cite{albritton2021non}, the solutions we construct live at a supercritical scaling, in which the
Externí odkaz:
http://arxiv.org/abs/2209.08713
We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-uniqueness discovered by the authors in [1].
Comment: Final versi
Comment: Final versi
Externí odkaz:
http://arxiv.org/abs/2209.03530
The Obukhov-Corrsin theory of scalar turbulence [Obu49, Cor51] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analogue for passive scalars of Kolmogorov's K41 theory of fully developed t
Externí odkaz:
http://arxiv.org/abs/2207.06833