3 citations · 5 across the 5 of their papers we have counts for
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Low regularity of non- local solutions to gMHD-alpha systems
Lorenzo Riva, Nathan Pennington
The Magneto-Hydrodynamic (MHD) system of equations governs viscous fluids subject to a magnetic field and is derived via a coupling of the Navier-Stokes equations and Maxwell's equ…
Local and Global low-regularity solutions to the Generalized Leray-alpha equations
Nathan Pennington
It has recently become common to study many different approximating equations of the Navier-Stokes equation. One of these is the Leray- equation, which regularizes the Navier-St…
Global Solutions to the Lagrangian Averaged Navier-Stokes equation in low regularity Besov spaces
Nathan Pennington
The Lagrangian Averaged Navier-Stokes (LANS) equations are a recently derived approximation to the Navier-Stokes equations. Existence of global solutions for the LANS equation has…
Local and global existence for the Lagrangian Averaged Navier-Stokes equations in Besov spaces
Nathan Pennington
We prove the existence of short time solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equation with low regularity initial data in Besov spaces $B^{r}_{…
Lagrangian Averaged Navier-Stokes equations with rough data in Sobolev space
Nathan Pennington
We prove the existence of short time, low regularity solutions to the incompressible, isotropic Lagrangian Averaged Navier-Stokes equations with initial data in Sobolev spaces. In…