## Some notes to the transport equation and to the Green formula.(English)Zbl 1165.35427

From the abstract: V. Girault and L. R. Scott [J. Math. Pures Appl. (9) 78, No. 10, 981–1011 (1999; Zbl 0961.35116)] claimed that in order to obtain a particular form of the Green formula for $$p=2$$ it is necessary to use the uniqueness result for the steady transport equation. Our aim is to generalize these results for $$p\in(1,\infty)$$ and show the Green formula without the use of the steady transport equation.

### MSC:

 35Q30 Navier-Stokes equations 35A08 Fundamental solutions to PDEs

Zbl 0961.35116
Full Text:

### References:

 [1] H. Beirão Da Veiga H. , Existence results in Sobolev spaces for a stationary transport equation , Ricerche di Mathematica , Vol. in honour of Prof. Miranda ( 1987 ), pp. 173 - 184 . MR 956025 | Zbl 0691.35087 · Zbl 0691.35087 [2] R.J. Diperna - P. L. LIONS, Ordinary differential equations, transport theory and Sobolev spaces , Invent. Math. , 98 ( 1989 ), pp. 511 - 547 . MR 1022305 | Zbl 0696.34049 · Zbl 0696.34049 [3] V. Girault - L.R. Scott , Analysis of a two dimensional grade-two fluid model with a tangential boundary condition , Journal des Math. Pures et Appl. , 78 ( 1999 ), pp. 981 - 1011 . MR 1732050 | Zbl 0961.35116 · Zbl 0961.35116 [4] A. Novotný : About the steady transport equation , in: Proceedings of Fifth Winter School at Paseky, Pitman Research Notes in Mathematics ( 1998 ), pp. 118 - 146 . MR 1692347 | Zbl 0941.35079 · Zbl 0941.35079 [5] J.P. Puel - M.C. Roptin , Lemme de Friedrichs. Théorème de densité résultant du Lemme de Friedrichs , Rapport de stage dirigé par C. Goulaouic, DEA Université de Rennes ( 1967 ).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.