2012
DOI: 10.1016/j.jmaa.2012.01.028
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Global existence and optimal L2 decay rate for the strong solutions to the compressible fluid models of Korteweg type

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Cited by 45 publications
(9 citation statements)
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“…Compared with [13,19], in theorems 1.1 and 1.2, we obtain the global wellposedness and the optimal time decay rates for multi-dimensional non-conservative viscous compressible two-uid system (1.1) in critical regularity framework respectively. Additionally, in theorem 1.2, the regularity index s can take both negative and nonnegative values, rather than only nonnegative integers, which improves the classical decay results in high Sobolev regularity, such as [13,19,45,46].…”
Section: Introduction and Main Resultsmentioning
confidence: 91%
“…Compared with [13,19], in theorems 1.1 and 1.2, we obtain the global wellposedness and the optimal time decay rates for multi-dimensional non-conservative viscous compressible two-uid system (1.1) in critical regularity framework respectively. Additionally, in theorem 1.2, the regularity index s can take both negative and nonnegative values, rather than only nonnegative integers, which improves the classical decay results in high Sobolev regularity, such as [13,19,45,46].…”
Section: Introduction and Main Resultsmentioning
confidence: 91%
“…The pointwise estimate (21) together with the solution formula (12) gives the corresponding pointwise estimates forĜ andĤ. The result is stated as follows.…”
Section: Decay Propertiesmentioning
confidence: 96%
“…The system was derived rigorously by Dunn and Serrin [1], see also [2,3]. Equation (1) has attracted interests of lots of mathematicians and physicists and some important results were made, we may refer to [4][5][6][7][8][9][10][11][12][13][14][15][16].…”
Section: Introductionmentioning
confidence: 99%
“…We also mention the work by Kawashima [19,20,36], where L 2estimates for general hyperbolic-parabolic systems were studied by applying Fourier analysis to the linearised homogeneous system. And for the works on the large-time behavior of solutions to some models related to the compressible Navier-Stokes equations, see, for instance, [6,22,28,37,38] and references therein.…”
Section: Introductionmentioning
confidence: 99%