A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL LP FRAMEWORK

doi:10.1007/s10473-019-0614-7

Abstract

Abstract: The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin[12], which can be used as a phase transition model. Motivated by[9], we aim at extending the work by Danchin-Desjardins[11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms, we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.

Key words: Korteweg system, global existence, L^p-type Besov norms

CLC Number:

35B40

Zhensheng GAO, Yan LIANG, Zhong TAN. A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK[J].Acta mathematica scientia,Series B, 2019, 39(6): 1639-1660.

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References

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A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK

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