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Existence and time-asymptotics of global strong solutions to dynamic Korteweg models

Existence and time-asymptotics of global strong solutions to dynamic Korteweg models

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KOTSCHOTE, Matthias, 2014. Existence and time-asymptotics of global strong solutions to dynamic Korteweg models. In: Indiana University Mathematics Journal. 63(1), pp. 21-51. ISSN 0022-2518. eISSN 1943-5274. Available under: doi: 10.1512/iumj.2014.63.5187

@article{Kotschote2014Exist-30157, title={Existence and time-asymptotics of global strong solutions to dynamic Korteweg models}, year={2014}, doi={10.1512/iumj.2014.63.5187}, number={1}, volume={63}, issn={0022-2518}, journal={Indiana University Mathematics Journal}, pages={21--51}, author={Kotschote, Matthias} }

In this paper, we investigate isothermal and non-isothermal models of capillary compressible fluids as derived by J. E. Dunn and J. Serrin (1985). We establish global existence and uniqueness for initial data near equilibria, and show exponential stability of equilibrias in the phase space. The proof is based on maximal L<sub>p</sub>-regularity results for the associated linear problem. 2014 2015-03-04T15:13:28Z Kotschote, Matthias Existence and time-asymptotics of global strong solutions to dynamic Korteweg models Kotschote, Matthias eng 2015-03-04T15:13:28Z

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