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Local weak solution of the isentropic compressible Navier–Stokes equations.
- Source :
-
Journal of Mathematical Physics . Nov2021, Vol. 62 Issue 11, p1-8. 8p. - Publication Year :
- 2021
-
Abstract
- Whether the three dimensional isentropic compressible Navier–Stokes equations admit weak solutions for arbitrary initial data with adiabatic exponent γ > 1 remains a challenging problem. The only available results under γ > 1 were achieved by either assuming the initial data with small energy due to Hoff [J. Differ. Equations 120(1), 215–254 (1995)] or under the spherically symmetric condition by Jiang and Zhang [Commun. Math. Phys. 215, 559–581 (2001)] and Huang [J. Differ. Equations 262, 1341–1358 (2017)]. In this paper, we establish the existence of weak solutions with higher regularity of the three-dimensional periodic compressible isentropic Navier–Stokes equations in small time for the adiabatic exponent γ > 1 in the presence of vacuum. It can be viewed as a local version of Hoff's work and also extends the result of Desjardins [Commun. Partial Differ. Equations 22(5–6), 977–1008 (1997)] by removing the assumption of γ > 3. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MATHEMATICS
*EQUATIONS
*EXPONENTS
Subjects
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 62
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 153907477
- Full Text :
- https://doi.org/10.1063/5.0054450