Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients

By Raphaël Danchin. 2005

63 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/790d95843df9117b555f49ffabc22c51b2656ae0

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In Applied Mathematics

1. Marius Paicu
2. Ian Tice
3. Yan Guo
4. Ping Zhang
5. Raphaël Danchin
6. Clément Mouhot
7. Yanjin Wang
8. Hammadi Abidi

In Mathematical Physics

1. Marius Paicu
2. Yan Guo
3. Ian Tice
4. Ping Zhang
5. Raphaël Danchin
6. Hammadi Abidi
7. Thomas Alazard
8. Yanjin Wang

Citations in the corpus

• Existence and uniqueness results for the Boussinesq system with data in Lorentz spaces (2008, unknown): “12 in [9]).”
• Decay of viscous surface waves without surface tension (2010, unknown): “1 of [10] along with the embedding H3/2 ↪→ B1 2,∞ ∩ L∞.”
• Global Well-posedness of Incompressible Inhomogeneous Fluid Systems with Bounded Density or Non-Lipschitz Velocity (2012, unknown): “33 of [6] (see also [12]) implies that ‖a‖ L̃∞t (B d q + ε 2 q,∞ ) Cε‖a0‖ B d q +ε q,∞ × exp { Cε(‖u‖ L̃(1)t (Ḃ 1+ p −ε p,r ) + ‖u‖ L̃(1)t (Ḃ 1+ p p,r ) ) } , (5.”
• Local well-posedness of the viscous surface wave problem without surface tension (2013, methodology): “Note that the result in [13] is stated for Σ = R2, but the same result holds in the periodic setting Σ = (L1T)× (L2T), as described in [14].”
• Almost Exponential Decay of Periodic Viscous Surface Waves without Surface Tension (2013, background): “1 of [9] along with the embedding H3/2 ↪→ B1 2,∞ ∩ L∞.”
• 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, background): “De ce fait, le champ de vitesses est presque localement intégrable en temps à valeurs quasi-lipschitziennes et l’on peut faire appel à des estimations avec perte de régularité dans l’esprit de celles qui ont été établies dans [2] ou, plus récemment, dans [12].”
• GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO (2008, background): “For the transport equation, we shall prove the following result (in the spirit of [3, 12]).”
• 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…”