Classical flows of vector fields with exponential or sub-exponential summability
Ambrosio, L., Nicolussi Golo, S., & Serra Cassano, F. (2023). Classical flows of vector fields with exponential or sub-exponential summability. Journal of Differential Equations, 372(5), 458-504. https://doi.org/10.1016/j.jde.2023.07.005
Julkaistu sarjassa
Journal of Differential EquationsPäivämäärä
2023Tekijänoikeudet
© 2023 The Authors. Published by Elsevier Inc.
We show that vector fields b whose spatial derivative Dx b satisfies a Orlicz summability condition have a spatially continuous representative and are well-posed. For the case of sub-exponential summability, their flows satisfy a Lusin (N) condition in a quantitative form, too. Furthermore, we prove that if Dx b satisfies a suitable exponential summability condition then the flow associated to b has Sobolev regularity, without assuming boundedness of divx b. We then apply these results to the representation and Sobolev regularity of weak solutions of the Cauchy problem for the transport and continuity equations.
Julkaisija
Elsevier BVISSN Hae Julkaisufoorumista
0022-0396Asiasanat
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https://converis.jyu.fi/converis/portal/detail/Publication/184006724
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