Local weak solution of the isentropic compressible Navier–Stokes equations
- 1 November 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (11), 111504
- https://doi.org/10.1063/5.0054450
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.Funding Information
- National Natural Science Foundation of China (11971464, 11688101, 11731007, 11871113, 11371064)
- K. C. Wong Education Foundation
- Youth Innovation Promotion Association
This publication has 14 references indexed in Scilit:
- Global well‐posedness of classical solutions with large oscillations and vacuum to the three‐dimensional isentropic compressible Navier‐Stokes equationsCommunications on Pure and Applied Mathematics, 2011
- Dynamics of singularity surfaces for compressible, viscous flows in two space dimensionsCommunications on Pure and Applied Mathematics, 2002
- On the Existence of Globally Defined Weak Solutions to the Navier—Stokes EquationsJournal of Mathematical Fluid Mechanics, 2001
- Regularity of weak solutions of the compressible isentropic navier-stokes equationsCommunications in Partial Differential Equations, 1997
- On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluidSiberian Mathematical Journal, 1995
- Global Solutions of the Navier-Stokes Equations for Multidimensional Compressible Flow with Discontinuous Initial DataJournal of Differential Equations, 1995
- Long time behavior for one-dimensional motion of a general barotropic viscous fluidArchive for Rational Mechanics and Analysis, 1989
- An existence theorem for compressible viscous fluidsAnnali di Matematica Pura ed Applicata (1923 -), 1982
- Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluidJournal of Mathematical Sciences, 1980
- On the Cauchy problem for the system of fundamental equations describing the movement of compressible viscous fluidKodai Mathematical Journal, 1971