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The idea is to approximate the vorticity by convolving it with a cutoff function.
Let be a cutoff function satisfying (2.6).
We may choose the test function in Definition 1.1, where is a cutoff function satisfying (3.2).
for any constant, where and is a cutoff function satisfying (2.2).
where is a cutoff function identically equal to 1 in and identically equal to 0 outside.
Here log+t is a cutoff function such that log+t = 1 for t ≤ e otherwise log+t = log t.
Similar(49)
Following [30], we put begin{aligned} tau = frac{1}{m}, e^{-frac{m^2}+zeta}+zeta }. end{aligned}Let (psi : mathbb{R } rightarrow [0,1]) be a smooth cutoff function such that (psi = 1) on ((-infty,1]) and (psi = 0) on ([2,infty )).
Using both an eighth order cutoff function and an infinite order cutoff function, we obtain low errors and high rates of convergence.
We also present an eighth order cutoff function with compact support.
where t α χ(t) is a smooth non-negative cutoff function identically equal to 1 for t ≤ 1 and identically equal to 0 for t ≥ 2. It is easy to check that there exists a constant c = c > 0, independent of σ ≥ 1, such that (19).
Fire brigades in London and Buckinghamshire have been called out to fires caused by the battery pack or charger overheating and having no safety cutoff function, while a Kent family suffered £25,000 of damage to their house after a hoverboard exploded in their kitchen.
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