Global smooth solutions in \(\mathbb{R}^3\) to short wave-long wave interactions systems for viscous compressible fluids (Q2878988)
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scientific article; zbMATH DE number 6340700
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Global smooth solutions in \(\mathbb{R}^3\) to short wave-long wave interactions systems for viscous compressible fluids |
scientific article; zbMATH DE number 6340700 |
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5 September 2014
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compressible Navier-Stokes equations
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nonlinear Schrödinger equations
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global regularity
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optimal decay rates
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Global smooth solutions in \(\mathbb{R}^3\) to short wave-long wave interactions systems for viscous compressible fluids (English)
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The authors study the Cauchy problem of Benney-type models describing short wave-long wave interactions for viscous compressible fluids, which consists of the Navier-Stokes equations for a heat conductive gas coupled with a nonlinear Schrödinger equations. When the initial data are small smooth perturbations of an equilibrium state, it was shown that there exists a unique global smooth solution to the three-dimensional Cauchy problem. Finally, some decay estimates are obtained.
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