Abstract
It is showed that, as the Mach number goes to zero, the weak solution of the compressible Navier-Stokes equations in the whole space with general initial data converges to the strong solution of the incompressible Navier-Stokes equations as long as the later exists. The proof of the result relies on the new modulated energy functional and the Strichartz’s estimate of linear wave equation.
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Project supported by the National Natural Science Foundation of China (Nos. 10431060, 10701011, 10501047) and the Nanjing University Talent Development Foundation.
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Hsiao, L., Ju, Q. & Li, F. The incompressible limits of compressible Navier-Stokes equations in the whole space with general initial data. Chin. Ann. Math. Ser. B 30, 17–26 (2009). https://doi.org/10.1007/s11401-008-0039-4
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DOI: https://doi.org/10.1007/s11401-008-0039-4
Keywords
- Compressible Navier-Stokes equations
- Incompressible Navier-Stokes equations
- Low Mach number limit
- Modulated energy functional
- Strichartz’s estimate