### Abstract

We prove the uniqueness of mild solutions and very weak solutions of the Navier-Stokes equations in C([0, T); L^{N}(Ω)), where Ω is the whole space ℝ^{N}, a regular domain of ℝ^{N} or the torus double-struck T sign^{N} with N ≥ 3. The proof relies upon three elementary ingredients: the introduction of a "dual" problem, a decomposition of the solutions and a "bootstrap" argument.

Original language | English (US) |
---|---|

Pages (from-to) | 2211-2226 |

Number of pages | 16 |

Journal | Communications in Partial Differential Equations |

Volume | 26 |

Issue number | 11-12 |

State | Published - 2001 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Analysis
- Applied Mathematics

### Cite this

*Communications in Partial Differential Equations*,

*26*(11-12), 2211-2226.

**Uniqueness of mild solutions of the Navier-Stokes system in LN
.** / Lions, P. L.; Masmoudi, N.

Research output: Contribution to journal › Article

*Communications in Partial Differential Equations*, vol. 26, no. 11-12, pp. 2211-2226.

}

TY - JOUR

T1 - Uniqueness of mild solutions of the Navier-Stokes system in LN

AU - Lions, P. L.

AU - Masmoudi, N.

PY - 2001

Y1 - 2001

N2 - We prove the uniqueness of mild solutions and very weak solutions of the Navier-Stokes equations in C([0, T); LN(Ω)), where Ω is the whole space ℝN, a regular domain of ℝN or the torus double-struck T signN with N ≥ 3. The proof relies upon three elementary ingredients: the introduction of a "dual" problem, a decomposition of the solutions and a "bootstrap" argument.

AB - We prove the uniqueness of mild solutions and very weak solutions of the Navier-Stokes equations in C([0, T); LN(Ω)), where Ω is the whole space ℝN, a regular domain of ℝN or the torus double-struck T signN with N ≥ 3. The proof relies upon three elementary ingredients: the introduction of a "dual" problem, a decomposition of the solutions and a "bootstrap" argument.

UR - http://www.scopus.com/inward/record.url?scp=0344509270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344509270&partnerID=8YFLogxK

M3 - Article

VL - 26

SP - 2211

EP - 2226

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 11-12

ER -