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Showing content from https://doi.org/10.1007/BF01393835 below:

Ordinary differential equations, transport theory and Sobolev spaces

We obtain some new existence, uniqueness and stability results for ordinary differential equations with coefficients in Sobolev spaces. These results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions.

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1. Beck, A.: Uniqueness of flow solutions of differential equations. In: Recent Advances in Topological Dynamics, (Lect. Notes Math. 318). Berlin, Heidelberg, New York: Springer 1973

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2. DiPerna, R.J., Lions, P.L.: On the Cauchy problem for Boltzmann equations: global existence and weak stability. Ann. Math. (to appear); see also C.R. Acad. Sci. Paris306, 343–346, (1988) and In Séminaire EDP, Ecole Polytechnique, 1987–88, Palaiseau

3. DiPerna, R.J., Lions, P.L.: On Fokker-Planck-Boltzmann equations. Commun. Math. Phys. (1989)

4. DiPerna, R.J., Lions, P.L.: Global weak solutions of Vlasov Maxwell systems. Commun. Phys. Appl. Math. (to appear)

5. DiPerna, R.J., Lions, P.L.: In preparation, see also C.R. Acad. Sci. Paris307, 655–658 (1988)

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6. DiPerna, R.J., Lions, P.L.: In preparation, see also in Séminaire EDP, Ecole Polytechnique, 1988–89, Palaiseau

7. DiPerna, R.J., Lions, P.L.: In preparation, see also in Séminaire EDP, Ecole Polytechnique, 1988–89, Palaiseau

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1. Department of Mathematics, University of Berkeley, 94720, Berkeley, CA, USA

   R. J. DiPerna

2. Ceremade, Université de Paris-Dauphine, Place de Lattre de Tassigny, F-75775, Paris Cedex 16, France

   P. L. Lions

1. R. J. DiPerna
2. P. L. Lions

DiPerna, R.J., Lions, P.L. Ordinary differential equations, transport theory and Sobolev spaces. Invent Math 98, 511–547 (1989). https://doi.org/10.1007/BF01393835

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• Issue Date: October 1989

• DOI: https://doi.org/10.1007/BF01393835

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