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- W2790056801 abstract "Let $L$ be a Neumann operator of the form $L=-Delta_{N}$ acting on $L^2(mathbb R^n)$. Let ${BMO}_{Delta_{N}}(mathbb R^n)$ denote the BMO space on $mathbb R^n$ associated to the Neumann operator $L$. In this article we will show that a function $fin { BMO}_{Delta_{N}}(mathbb R^n)$ is the trace of the solution of $${mathbb L}u=u_{t}+L u=0, u(x,0)= f(x),$$ where $u$ satisfies a Carleson-type condition begin{eqnarray*} sup_{x_B, r_B} r_B^{-n}int_0^{r_B^2}int_{B(x_B, r_B)} |nabla u(x,t)|^2 {dx dt } leq C 0$. Conversely, this Carleson condition characterizes all the ${mathbb L}$-carolic functions whose traces belong to the space ${BMO}_{Delta_{N}}(mathbb R^n)$. This result extends the analogous characterization founded by E. Fabes and U. Neri in ({Duke Math. J.} {42} (1975), 725-734) for the classical BMO space of John and Nirenberg. Furthermore, based on the characterization of ${BMO}_{Delta_{N}}(mathbb R^n)$ space mentioned above, we prove global well-posedness for parabolic equations of Navier-Stokes type with the Neumann boundary condition under smallness condition on intial data $u_{0}in {{ BMO}_{Delta_{N}}^{-1}(mathbb R^n)}$, which is motivated by the work of P. Auscher and D. Frey ({J. Inst. Math. Jussieu} {16(5)} (2017), 947-985)." @default.
- W2790056801 created "2018-03-29" @default.
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- W2790056801 date "2018-03-13" @default.
- W2790056801 modified "2023-09-27" @default.
- W2790056801 title "Application BMO type space to parabolic equations of Navier-Stokes type with the Neumann boundary condition" @default.
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