J. P. Davies

most citedNavier-Stokes blow-up rates in certain Besov spaces whose regularity exceeds the critical value by

ε \in [1, 2]

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math.AP2022

Properties of Navier-Stokes mild solutions in sub-critical Besov spaces whose regularity exceeds the critical value by $ε \in (0, 1)$

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…

math.AP2022★ 1 cited

Navier-Stokes blow-up rates in certain Besov spaces whose regularity exceeds the critical value by $ε \in [1, 2]$

Joseph P. Davies, Gabriel S. Koch

For a solution $u$ to the Navier-Stokes equations in spatial dimension $n \geq 3$ which blows up at a finite time $T > 0$ , we prove the blowup estimate ${\|u(t)\|}_{\dot{B}_{p,q}^{s_{p…

math.AP2021

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 $f \in L^{2} (R^{n})$ ( $n \geq 2$ ), we prove that if $p \in (n, \infty]$ , any solution $u\in L_{t}^{\infty}L_{x}^{2}\cap L_{t}^{2}H_{x}^{1}\cap L_{t}^{\frac{2p}{p…

math.AP2021

Properties of Navier-Stokes mild solutions with initial data in subcritical Lorentz spaces

Joseph P. Davies, Gabriel S. Koch

For initial data $f$ in a subcritical Lorentz space $L^{p, q} (R^{n}) ↪ B ˙_{\infty, \infty}^{- \frac{n}{p}} (R^{n})$ ( $n < p < \infty$ , $1 \leq q \leq \infty$ )…

Properties of Navier-Stokes mild solutions in sub-critical Besov spaces whose regularity exceeds the critical value by ε∈(0,1)

Navier-Stokes blow-up rates in certain Besov spaces whose regularity exceeds the critical value by ε∈[1,2]

Notions of solution and weak-strong uniqueness criteria for the Navier-Stokes equations in Lorentz spaces

Properties of Navier-Stokes mild solutions with initial data in subcritical Lorentz spaces

Properties of Navier-Stokes mild solutions in sub-critical Besov spaces whose regularity exceeds the critical value by $ε \in (0, 1)$

Navier-Stokes blow-up rates in certain Besov spaces whose regularity exceeds the critical value by $ε \in [1, 2]$