Zobrazeno 1 - 10
of 124
pro vyhledávání: '"Spirito, Stefano"'
Publikováno v:
Mathematics in Engineering 6(4), 494-509 (2024)
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
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
Autor:
Berselli, Luigi C., Spirito, Stefano
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefore suitable in the sense of Scheffer and Caffarelli-Kohn-Nirenberg. Mor
Externí odkaz:
http://arxiv.org/abs/2203.00462
We consider nonlinear viscoelastic materials of Kelvin-Voigt type with stored energies satisfying an Andrews-Ball condition, allowing for non convexity in a compact set. Existence of weak solutions with deformation gradients in $H^1$ is established f
Externí odkaz:
http://arxiv.org/abs/2012.10344
The relaxation-time limit from the Quantum-Navier-Stokes-Poisson system to the quantum drift-diffusion equation is performed in the framework of finite energy weak solutions. No assumptions on the limiting solution are made. The proof exploits the su
Externí odkaz:
http://arxiv.org/abs/2011.15054
Publikováno v:
Arch. Rational Mech. Anal. 240, 295-326 (2021)
In this paper we prove the uniform-in-time $L^p$ convergence in the inviscid limit of a family $\omega^\nu$ of solutions of the $2D$ Navier-Stokes equations towards a renormalized/Lagrangian solution $\omega$ of the Euler equations. We also prove tha
Externí odkaz:
http://arxiv.org/abs/2008.12133
We prove global existence of finite energy weak solutions to the quantum Navier-Stokes equations in the whole space with non trivial far-field condition in dimensions d = 2,3. The vacuum regions are included in the weak formulation of the equations.
Externí odkaz:
http://arxiv.org/abs/2001.01652
Publikováno v:
J. Nonlinear Sci. 30, 2787-2820 (2020)
We discuss the Lagrangian property and the conservation of the kinetic energy for solutions of the 2D incompressible Euler equations. Existence of Lagrangian solutions is known when the initial vorticity is in $L^p$ with $1\leq p\leq \infty$. Moreove
Externí odkaz:
http://arxiv.org/abs/1905.09720
Autor:
Antonelli, Paolo, Spirito, Stefano
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary to previous
Externí odkaz:
http://arxiv.org/abs/1903.02441
Smooth approximation is not a selection principle for the transport equation with rough vector field
Publikováno v:
Calc. Var. 59, 13 (2020)
In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the equation with a regularized vector field converge to a unique limit,
Externí odkaz:
http://arxiv.org/abs/1902.08084