4 citations · 4 across the 4 of their papers we have counts for
5 papers
Finite time blow-up for some parabolic systems arising in turbulence theory
Francesco Fanelli, Rafael Granero-Belinchón
We study a class of non-linear parabolic systems relevant in turbulence theory. Those systems can be viewed as simplified versions of the Prandtl one-equation and Kolmogorov two-eq…
A nonlocal model describing tumor angiogenesis
Rafael Granero-Belinchón
In this paper we study the onset of angiogenesis and derive a new model to describe it. This new model takes the form of a nonlocal Burgers equation with both diffusive and dispers…
A unified approach towards the impossibility of finite time vanishing depth for incompressible free boundary flows
Zhiyuan Geng, Rafael Granero-Belinchón
In this paper we study the motion of an internal water wave and an internal wave in a porous medium. For these problems we establish that, if the free boundary and, in the case of…
Interfaces in incompressible flows
Rafael Granero-Belinchón
The motion of both internal and surface waves in incompressible fluids under capillary and gravity forces is a major research topic. In particular, we review the derivation of some…
Well-posedness and singularity formation for the Kolmogorov two-equation model of turbulence in 1-D
Francesco Fanelli, Rafael Granero-Belinchón
We study the Kolomogorov two-equation model of turbulence in one space dimension. Two are the main results of the paper. First of all, we establish a local well-posedness theory in…