On the uniqueness in critical spaces for compressible Navier-Stokes equations

By Raphaël Danchin. 2005

115 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c1be595d0ae315bab846a2ffd638db8fad04cbd5

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In Applied Mathematics

1. Xianpeng Hu
2. Dehua Wang
3. Jinlu Li
4. Frédéric Charve
5. Zhaoyang Yin
6. Wenke Tan
7. Raphaël Danchin
8. Boris Haspot

In Control and Systems Engineering

1. Dehua Wang
2. Xianpeng Hu
3. Frédéric Charve
4. Zhaoyang Yin
5. Raphaël Danchin
6. Ping Zhang
7. Marius Paicu
8. Zhifei Zhang

In Mathematical Physics

1. Xianpeng Hu
2. Jinlu Li
3. Dehua Wang
4. Zhaoyang Yin
5. Frédéric Charve
6. Yue Liu
7. Wenke Tan
8. Raphaël Danchin

Citations in the corpus

• Global Existence for the Multi-Dimensional Compressible Viscoelastic flows (2010, methodology): “The proof of uniqueness will be same as in [3] with a slightly modification due to the deformation gradient.”
• A Global Existence Result for the Compressible Navier–Stokes Equations in the Critical Lp Framework (2010, background): “Uniqueness is a mere consequence of prior works (see [9]).”
• Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density (2007, background): “In Danchin (2001, 2005b) however, we had to make the additional assumption that − is small in Ḃ N p p 1 The reason why is that we handled the elliptic operator in the momentum equation of (NSC) as a constant coefficient second order operator plus a perturbation induced by − which, if sufficiently…”
• Local existence and uniqueness for the non-resistive MHD equations in homogeneous Besov spaces (2016, background): “8 in [6]) Let s ∈ (−dmin{(1) p , 1− 1 p } − 1, 1 + d p ), 1 ≤”
• Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces (2008, unknown): “On the other hand, due to the weak regularity assumptions, we shall be in the limit case for product laws in Proposition 4 so that a logarithmic interpolation argument (similar to that which has been used in [8] and [10]) will be required.”
• Les theoremes de Leray et de Fujita-Kato pour le systeme de Boussinesq partiellement visqueux. The Leray and Fujita-Kato theorems for the Boussinesq system with partial viscosity (2008, unknown): “On munit GT de la norme ‖(θ, u,∇Π)‖GT := ‖θ‖L∞T (Ḃ N,∞) + ‖u‖L∞T (Ḃ N,∞) + ν‖u‖e L(1)T (Ḃ1 N,∞) + ‖∇Π‖e L(1)T (Ḃ N,∞) Pour montrer l’unicité dans GT , nous allons suivre l’approche utilisée dans [13] : établir une inégalité différentielle sur ‖(δθ, δu,∇δΠ)‖GT grâce à un argument d’interpolation loga”
• Global well‐posedness for compressible Navier‐Stokes equations with highly oscillating initial velocity (2009, unknown): “[14] Let s ∈ (−nmin((1) p , 1 p ), 1 + n p ), and 1 ≤ p, q ≤ +∞.”