6 citations · 8 across the 5 of their papers we have counts for
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On the supnorm form of Leray's problem for the incompressible Navier-Stokes equations
Lineia Schutz, Janaína P. Zingano, Paulo R. Zingano
We show that t^{3/4}|| u(.,t) ||_{sup} --> 0 as t --> infty for all (global) Leray solutions of the incompressible Navier-Stokes equations in R3. It is also shown that t || u(.,t)…
On the global solvability of porous media equations with general (spatially dependent) advection terms
N. M. L. Diehl, L. Fabris, P. R. Zingano
We show that advection-diffusion equations with porous media type diffusion and integrable initial data are globally solvable under very mild conditions. Some generalizations and r…
Two problems in Partial Differential Equations (in Portuguese)
Paulo R. Zingano
In this work, we examine two important problems in the theory of nonlinear PDEs. In Part I, we propose and solve a more general and complete version of the celebrated Leray's probl…
An inequality for solutions of the Navier-Stokes equations in Rn
Thomas Hagstrom, Jens Lorenz, Janaína P. Zingano +1
We obtain a new inequality that holds for general Leray solutions of the incompressible Navier-Stokes equations in Rn (n <= 4). This recovers important results previously obtained…
Some remarks on the regularity time of Leray solutions to the Navier-Stokes equations
Pablo Braz e Silva, Janaína P. Zingano, Paulo R. Zingano
In this small note we strengthen the classic result about the regularity time t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations in Rn (n = 3, 4), whic…
The Navier-Stokes equations for Incompressible Flows: solution properties at potential blow-up times
Jens Lorenz, Paulo R. Zingano
In this paper we consider the Cauchy problem for the 3D Navier-Stokes equations for incompressible flows. The initial data are assumed to be smooth and rapidly decaying at infinity…