New functional inequality and its application
Résumé
In this short note, we prove by simple arguments a new kind of Logarithmic Sobolev inequalities generalizing two known inequalities founded in some papers related to fluid dynamics models (see for instance [6] and [3]). As a by product, we show how our inequality can help in obtaining some important a priori estimates for the solution of the Navier-Stokes-Korteweg system.
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