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pro vyhledávání: '"Davies, Joseph"'
Autor:
Davies, Joseph P., Koch, Gabriel S.
We consider mild solutions to the Navier-Stokes initial-value problem which belong to certain ranges $Z_{p,q}^{s}(T,n):=\widetilde{L}^{1}(0,T;\dot{B}_{p,q}^{s+2}(\mathbb{R}^{n}))\cap\widetilde{L}^{\infty}(0,T;\dot{B}_{p,q}^{s}(\mathbb{R}^{n}))$ of Ch
Externí odkaz:
http://arxiv.org/abs/2212.12344
Autor:
Davies, Joseph P., Koch, Gabriel S.
Publikováno v:
SIAM Journal on Mathematical Analysis, 2023
For a solution $u$ to the Navier-Stokes equations in spatial dimension $n\geq3$ which blows up at a finite time $T>0$, we prove the blowup estimate ${\|u(t)\|}_{\dot{B}_{p,q}^{s_{p}+\epsilon}(\mathbb{R}^n)}\gtrsim_{\varphi,\epsilon,(p\vee q\vee 2)}{(
Externí odkaz:
http://arxiv.org/abs/2203.12993
Autor:
Davies, Joseph P., Koch, Gabriel S.
For initial data $f\in L^{2}(\mathbb{R}^n)$ ($n\geq 2$), we prove that if $p\in(n,\infty]$, any solution $u\in L_{t}^{\infty}L_{x}^{2}\cap L_{t}^{2}H_{x}^{1}\cap L_{t}^{\frac{2p}{p-n}}L_{x}^{p,\infty}$ to the Navier-Stokes equations satisfies the ene
Externí odkaz:
http://arxiv.org/abs/2111.04350
Autor:
Davies, Joseph P., Koch, Gabriel S.
For initial data $f$ in a subcritical Lorentz space $L^{p,q}(\mathbb{R}^{n}) \hookrightarrow \dot B^{-\frac np}_{\infty,\infty}(\mathbb{R}^n)$ ($n
Externí odkaz:
http://arxiv.org/abs/2111.03520