A quantitative theory for the continuity equation

@article{Seis2016AQT,
  title={A quantitative theory for the continuity equation},
  author={Christian Seis},
  journal={arXiv: Analysis of PDEs},
  year={2016}
}
  • Christian Seis
  • Published 9 February 2016
  • Mathematics
  • arXiv: Analysis of PDEs
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Optimal stability estimates for continuity equations
  • Christian Seis
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2018
This review paper is concerned with the stability analysis of the continuity equation in the DiPerna–Lions setting in which the advecting velocity field is Sobolev regular. Quantitative estimates for
Estimates and regularity results for the DiPerna-Lions flow
Abstract In this paper we derive new simple estimates for ordinary differential equations with Sobolev coefficients. These estimates not only allow to recover some old and recent results in a simple
A new proof of the uniqueness of the flow for ordinary differential equations with BV vector fields
We provide in this article a new proof of the uniqueness of the flow solution to ordinary differential equations with BV vector fields that have divergence in L∞ (or in L1), when the flow is assumed
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We prove some theorems on the existence, uniqueness, stability and compactness properties of solutions to inhomogeneous transport equations with Sobolev coefficients, where the inhomogeneous term
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SummaryWe 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
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In this paper we review many aspects of the well-posedness theory for the Cauchy problem for the continuity and transport equations and for the ordinary differential equation (ODE). In this
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We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions (Invent Math 98:511–547, 1989) proved that, when the damping term
On the Cauchy problem for Boltzmann equations: global existence and weak stability
We study the large-data Cauchy problem for Boltzmann equations with general collision kernels. We prove that sequences of solutions which satisfy only the physically natural a priori bounds converge
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