42 citations · 181 across the 22 of their papers we have counts for
24 papers
Singularidades para as soluções das Equações de Navier-Stokes and Euler e o Problema do Milênio
Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
The purpose of this note is to offer a birds-eye view on the history and the state-of-the-art in the research surrounding the Millenium Prize problem for the Navier-Stokes equation…
Absence of anomalous dissipation for vortex sheets
Tarek Elgindi, Milton Lopes Filho, Helena Nussenzveig Lopes
A family of solutions of the incompressible Navier-Stokes equations is said to present anomalous dissipation if energy dissipation due to viscosity does not vanish in the limit of…
Improved regularity and analyticity of Cannone-Karch solutions of the three-dimensional Navier-Stokes equations on the torus
David M. Ambrose, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
We consider the three-dimensional Navier-Stokes equations, with initial data having second derivatives in the space of pseudomeasures. Solutions of this system with such data have…
Existence and analyticity of solutions of the Kuramoto-Sivashinsky equation with singular data
David M. Ambrose, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
We prove existence of solutions to the Kuramoto-Sivashinsky equation with low-regularity data, in function spaces based on the Wiener algebra and in pseudomeasure spaces. In any sp…
Large time behavior for the 3D Navier-Stokes with Navier boundary conditions
James P. Kelliher, Christophe Lacave, Milton C. Lopes Filho +2
We study the three-dimensional incompressible Navier-Stokes equations in a smooth bounded domain with initial velocity square-integrable, divergence-free and tangent to $…
The incompressible --Euler equations in the exterior of a vanishing disk
Adriana Valentina Busuioc, Dragos Iftimie, Milton Lopes Filho +1
In this article we consider the --Euler equations in the exterior of a small fixed disk of radius . We assume that the initial potential vorticity is compactly supported and…
Energy balance for forced two-dimensional incompressible ideal fluid flow
Milton Lopes Filho, Helena Nussenzveig Lopes
In [Commun Math Phys 348(1), 129-143, 2016], Cheskidov et al. proved that physically realizable weak solutions of the incompressible 2D Euler equations on a torus conserve kinetic…
The limit of vanishing viscosity for the incompressible 3D Navier-Stokes equations with helical symmetry
Quansen Jiu, Milton C. Lopes Filho, Dongjuan Niu +1
In this paper, we are concerned with the vanishing viscosity problem for the three-dimensional Navier-Stokes equations with helical symmetry, in the whole space. We choose viscosit…
Asymptotic behavior of 2D incompressible ideal flow around small disks
C. Lacave, M. C. Lopes Filho, H. J. Nussenzveig Lopes
In this article, we study the homogenization limit of a family of solutions to the incompressible 2D Euler equations in the exterior of a family of disjoint disks with center…
On the Onsager conjecture in two dimensions
A. Cheskidov, M. C. Lopes Filho, H. J. Nussenzveig Lopes +1
This note addresses the question of energy conservation for the 2D Euler system with an -control on vorticity. We provide a direct argument, based on a mollification in physic…
Uniform time of existence for the alpha Euler equations
A. V. Busuioc, D. Iftimie, M. C. Lopes Filho +1
We consider the -Euler equations on a bounded three-dimensional domain with frictionless Navier boundary conditions. Our main result is the existence of a strong solution on a p…
Approximation of 2D Euler Equations by the Second-Grade Fluid Equations with Dirichlet Boundary Conditions
Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Edriss S. Titi +1
The second-grade fluid equations are a model for viscoelastic fluids, with two parameters: , corresponding to the elastic response, and , corresponding to viscosity. Fo…
Convergence of the 2D Euler- to Euler equations in the Dirichlet case: indifference to boundary layers
Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Edriss S. Titi +1
In this article we consider the Euler- system as a regularization of the incompressible Euler equations in a smooth, two-dimensional, bounded domain. For the limiting Euler syst…
Serfati solutions to the 2D Euler equations on exterior domains
David M. Ambrose, James P. Kelliher, Milton C. Lopes Filho +1
We prove existence and uniqueness of a weak solution to the incompressible 2D Euler equations in the exterior of a bounded smooth obstacle when the initial data is a bounded diverg…
Wild solutions for 2D incompressible ideal flow with passive tracer
Anne Bronzi, Milton Lopes Filho, Helena Nussenzveig Lopes
In Ann. Math., 170 (2009), 1417-1436, C. De Lellis and L. Székelyhidi Jr. constructed wild solutions of the incompressible Euler equations using a reformulation of the Euler equati…
Global existence of a weak solution of the incompressible Euler equations with helical symmetry and vorticity
Anne C. Bronzi, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
We prove the global existence of a helical weak solution of the 3D Euler equations, in full space, for an initial velocity with helical symmetry, without swirl and whose initial vo…
Weak vorticity formulation for the incompressible Euler equations in domains with boundary
Dragos Iftimie, Milton Lopes Filho, Helena Nussenzveig Lopes +1
In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boun…
Planar limits of three-dimensional incompressible flows with helical symmetry
Milton C. Lopes Filho, Anna L. Mazzucato, Dongjuan Niu +2
Helical symmetry is invariance under a one-dimensional group of rigid motions generated by a simultaneous rotation around a fixed axis and translation along the same axis. The key…
Nonlinear stabilitty for steady vortex pairs
Geoffrey R. Burton, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensi…
Stability of Two-dimensional Viscous Incompressible Flows Under Three-dimensional Perturbations and Inviscid Symmetry Breaking
Claude Bardos, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes +2
In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine bot…
Weak stability of Lagrangian solutions to the semigeostrophic equations
Josiane C. O. Faria, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
In [1], Cullen and Feldman proved existence of Lagrangian solutions for the semigeostrophic system in physical variables with initial potential vorticity in , . Here, we…
Vanishing viscosity limit for an expanding domain in space
J. P. Kelliher, M. C. Lopes Filho, H. J. Nussenzveig Lopes
We study the limiting behavior of viscous incompressible flows when the fluid domain is allowed to expand as the viscosity vanishes. We describe precise conditions under which the…
Confinement of vorticity in two dimensional ideal incompressible exterior flow
D. Iftimie, M. C. Lopes Filho, H. J. Nussenzveig Lopes
In [Math. Meth. Appl. Sci. 19 (1996) 53-62], C. Marchioro examined the problem of vorticity confinement in the exterior of a smooth bounded domain. The main result in Marchioro's p…
Large time behavior for vortex evolution in the half-plane
D. Iftimie, M. C. Lopes Filho, H. J. Nussenzveig Lopes
In this article we study the long-time behavior of incompressible ideal flow in a half plane from the point of view of vortex scattering. Our main result is that certain asymptotic…