Global existence and asymptotic convergence of weak solutions for the one-dimensional Navier-Stokes equations with capillarity and nonmonotonic pressure |
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Authors: | Eugene Tsyganov |
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Affiliation: | Indiana University, E. 3rd Street, apt 09, Bloomington, IN 47401, USA |
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Abstract: | We construct global weak solution of the Navier-Stokes equations with capillarity and nonmonotonic pressure. The volume variable v0 is initially assumed to be in H1 and the velocity variable u0 to be in L2 on a finite interval [0,1]. We show that both variables become smooth in positive time and that asymptotically in time u→0 strongly in L2([0,1]) and v approaches the set of stationary solutions in H1([0,1]). |
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Keywords: | 35B35 35B40 76N10 |
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