Zobrazeno 1 - 10
of 911
pro vyhledávání: '"Colombo, Maria"'
We propose a new convex integration scheme in fluid mechanics, and we provide an application to the two-dimensional Euler equations. We prove the flexibility and nonuniqueness of $L^\infty L^2$ weak solutions with vorticity in $L^\infty L^p$ for some
Externí odkaz:
http://arxiv.org/abs/2408.07934
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
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