Sentence examples for established the estimates from inspiring English sources

They showed that the solution blows up in finite time T, established the estimates of the blow-up rates, and described the asymptotic behavior of the solution.

Chen and Zhang [18] established the estimate by the Littlewood-Paley trichotomy decomposition.

We establish the estimates of solution.

We need to establish the estimates for (phi_{lambda}).

In this subsection, we establish the estimates of horizontal spatial derivatives.

In the cases (0establish the estimates on the nonlinear term.

In this section, we establish the estimates for Lipschitz and BMO norms for the composite operator G ∘ P. We need the following lemmas and definition.

Now we establish the estimates and convergences for the velocity field (hat{u}^{varepsilon}) and the pressure (widehat{p}^{varepsilon}) in the domain Ω.

We first use an iteration method to establish the estimates of lower bounds of positive mild solutions, then we obtain the unboundedness of solutions for large time.

Now we are ready to establish the estimate on (int_{Omega}u^{m+1},dx+int_{Omega}|nabla v|^{4},dx).

In order to establish the estimate (3.7), it is enough to make use of (3.8) in (3.11).