Sentence examples for smooth solutions from inspiring English sources

For smooth solutions, Eqs.

Local existence of smooth solutions.

Then (1 -(4) admit global smooth solutions.

Existence and uniqueness for local smooth solutions.

A blow-up criterion of smooth solutions is obtained.

Two logarithmically blow-up criteria of smooth solutions are established.

The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable.

The results show exponential error convergence of order p + 1∕2 for smooth solutions.

Numerical examples show that the accordingly designed fluxes resolve discontinuities and smooth solutions very precisely.

Next, by the standard continuous arguments, we can obtain the global existence of smooth solutions.

For the 2D case, Ladyzhenskaya [1] solved the uniqueness of the global smooth solutions.