No blow-up to a variational wave equation in liquid crystals (Q2795516)
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scientific article; zbMATH DE number 6559011
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | No blow-up to a variational wave equation in liquid crystals |
scientific article; zbMATH DE number 6559011 |
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No blow-up to a variational wave equation in liquid crystals (English)
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21 March 2016
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liquid crystals
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variational wave equation
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Cauchy problem
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0.89626074
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0.8851813
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0.8851695
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0.88097596
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0.8806712
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0.88061154
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0.87903833
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0.8779475
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The authors consider the Cauchy problem of variational wave equations with one space dimension NEWLINE\[NEWLINEu_{tt}-c_1^2u_{xx}=aa^{\prime}(v_t^2-c_2^2v_x^2)-a^2c_2c_2^{\prime}v_x^2, NEWLINE\]NEWLINE NEWLINE\[NEWLINEv_{tt}-(c_2v_x)_x=0,NEWLINE\]NEWLINE where \(c_1\) is a positive number, \(c_2\) and \(a\) are positive smooth functions of \(u,\) modeling a type of nematic liquid crystals with equal splay and bend coefficients. The global existence of smooth solutions is established.
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