8 papers
Absence of local anomalous dissipation and local energy balance in 2D incompressible flows away from the boundary
Tobias Barker, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes
For the 2D Navier-Stokes equations with no-slip boundary condition, we consider the issue of whether anomalous dissipation away from the boundary vanishes. In particular, we show t…
Sharp conditions for energy balance in two-dimensional incompressible ideal flow with external force
Fabian Jin, Samuel Lanthaler, Milton C. Lopes Filho +1
Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where the rate-of-change in time of the kinetic energy equals the work done by the force pe…
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 $…
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…