×

zbMATH — the first resource for mathematics

On two-dimensional Hamiltonian transport equations with \(\mathbb L^p_{\text{loc}}\) coefficients. (English) Zbl 1028.35148
F. Bouchut and L. Desvillettes [Differ. Integral Equ. 14, 1015-1024 (2001; Zbl 1028.35042)] analysed the Hamiltonian transport equation with continuous coefficient. Their consideration based on the fact that the equivalent ordinary differential equation may be solved. Here this method is generalized for less regularity of the coefficients.

MSC:
35R05 PDEs with low regular coefficients and/or low regular data
82C70 Transport processes in time-dependent statistical mechanics
35F10 Initial value problems for linear first-order PDEs
PDF BibTeX XML Cite
Full Text: DOI Numdam EuDML arXiv
References:
[1] Adams, R.A., Sobolev spaces, (1975), Academic Press, p. 54 · Zbl 0186.19101
[2] Bouchut, F., Renormalized solutions to the vlassov equation with coefficients of bounded variation, Arch. rat. mech. anal., 157, 75-90, (2001) · Zbl 0979.35032
[3] Bouchut, F.; Desvillettes, L., On two-dimensional Hamiltonian transport equations with continuous coefficients, Differential integral equation, 14, 8, 1015-1024, (2001) · Zbl 1028.35042
[4] DiPerna, R.J.; Lions, P.L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. math., 98, 511-547, (1989) · Zbl 0696.34049
[5] Lions, P.L., Sur LES équations différentielles ordinaires et LES équations de transport, C. R. acad. sci. Paris, Série I, 326, 833-838, (1998) · Zbl 0919.34028
[6] Royden, H.L., Real analysis, (1963), The MacMullan Company, Chapter 14 · Zbl 0121.05501
[7] Ziemer, W.P., Weakly differentiable functions, (1989), GTM, Springer-Verlag, p. 44 · Zbl 0177.08006
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.