Name
Title | ||
|---|---|---|
Global Solutions to the Isentropic Compressible Navier--Stokes Equations with a Class of Large Initial Data |
Abstract | ||
|---|---|---|
this paper, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space R-N, with N >= 2. It is shown that the one-parameter group e(+/- it Lambda) is of great importance to the behaviors of solutions to the isentropic compressible Navier-Stokes equations in the low frequency part. In order to better reflect the dispersive property of this system, we introduce a new solution space that characterizes the behaviors of the solutions in different frequencies and prove that the isentropic compressible Navier-Stokes equations admit global solutions when the initial data are close to a stable equilibrium in the sense of suitable hybrid Besov norms. As a consequence, the initial velocity with an arbitrary (B) over dot(2,1)(N/2-1) norm of potential part P(perpendicular to)u(0) and a large highly oscillating initial velocity are allowed in our results. The proof relies heavily on the dispersive estimates for the system of acoustics and a careful study of the nonlinear terms. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M1122062 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
Keywords | Field | DocType |
compressible Navier-Stokes equations,global well-posedness,large data | Compressibility,Isentropic process,Compressible navier stokes equations,Oscillation,Dispersion relation,Nonlinear system,Mathematical analysis,Stable equilibrium,Mathematics | Journal |
Volume | Issue | ISSN |
50 | 5 | 0036-1410 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Daoyuan Fang | 1 | 1 | 2.12 |
| Ting Zhang | 2 | 5 | 2.79 |
| Ruizhao Zi | 3 | 0 | 0.34 |