In this section, we investigate the higher regularity and prove the maximum principle for the regularized system (1.3).
Next, we will apply (12) and (13) to improve the higher regularity on the velocity u and magnetic fields B, respectively.
The longer first step of anodization, the higher regularity ratio and circularity, and lower percentage of defects in the nanoporous array.
Normally the service was not chosen to be subject to strikes due to the high regularity needed by the chicken manufacturer Trønderkylling, who would otherwise have to proceed with unnecessary slaughtering of animals.
This is due to the fact that the angle entropy of the buried residues is lower than that of the exposed ones, demonstrating the higher regularities of the protein fragments in core regions.
Now, we end this section with the following lemma, which plays an important role in the proof of higher regularity of the pullback attractors.
The jury noted the system's high regularity, safety and passenger satisfaction, as well as the efficient transport to the airport.
The proposed architecture has the advantage of high regularity and a reduced hardware complexity based on combining the characteristics of the irreducible AOP and PCA.
Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map.
Stated simply, the high nonlinearity of the k-ε equations leads to the necessity of high regularity of some unknown functions and thus leads to much difficulties for the a priori estimates.
