64 citations · 240 across the 12 of their papers we have counts for
12 papers
Properties of Navier-Stokes mild solutions in sub-critical Besov spaces whose regularity exceeds the critical value by
Joseph P. Davies, Gabriel S. Koch
We consider mild solutions to the Navier-Stokes initial-value problem which belong to certain ranges $Z_{p,q}^{s}(T,n):=\widetilde{L}^{1}(0,T;\dot{B}_{p,q}^{s+2}(\mathbb{R}^{n}))\c…
Parabolic fractal dimension of forward-singularities for Navier-Stokes and liquid crystals inequalities
Gabriel S. Koch
In 1985, V. Scheffer discussed partial regularity results for what he called solutions to the "Navier-Stokes inequality". These maps essentially satisfy the incompressibility condi…
Navier-Stokes blow-up rates in certain Besov spaces whose regularity exceeds the critical value by
Joseph P. Davies, Gabriel S. Koch
For a solution to the Navier-Stokes equations in spatial dimension which blows up at a finite time , we prove the blowup estimate ${\|u(t)\|}_{\dot{B}_{p,q}^{s_{p…
Notions of solution and weak-strong uniqueness criteria for the Navier-Stokes equations in Lorentz spaces
Joseph P. Davies, Gabriel S. Koch
For initial data (), we prove that if , any solution $u\in L_{t}^{\infty}L_{x}^{2}\cap L_{t}^{2}H_{x}^{1}\cap L_{t}^{\frac{2p}{p…
Properties of Navier-Stokes mild solutions with initial data in subcritical Lorentz spaces
Joseph P. Davies, Gabriel S. Koch
For initial data in a subcritical Lorentz space (, )…
Partial regularity for Navier-Stokes and liquid crystals inequalities without maximum principle
Gabriel S. Koch
In 1985, V. Scheffer discussed partial regularity results for what he called solutions to the "Navier-Stokes inequality". These maps essentially satisfy the incompressibility condi…