Global regularity of density patch for the 3D inhomogeneous Navier–Stokes equations

Chen, Qionglei; Li, Yatao

doi:10.1007/s00033-020-1263-3

Cited by 2 publications

(1 citation statement)

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“…One can also refer to [20,22,35,36,34,7] concerning the global persistence of higher boundary regularity of the density patch. When ν = 0, the system (1.1) becomes the density-dependent incompressible Euler equations, which contains the classical incompressible Euler equations as a special case.…”

Section: Introductionmentioning

confidence: 99%

Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density

Li¹,

Miao²,

Xue³

2021

Preprint

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The paper concerns with the global well-posedness issue of the 2D incompressible inhomogeneous Navier-Stokes (INS) equations with fractional dissipation and rough density. We first establish the L q t (L p )-maximal regularity estimate for the generalized Stokes system with fractional dissipation, and then we employ it to obtain the global existence of solution for the 2D fractional INS equations with large velocity field, provided that the L 2 ∩ L ∞ -norm of density minus constant 1 is small enough. Moreover, by additionally assuming that the density minus 1 is sufficiently small in the norm of some multiplier spaces, we prove the uniqueness of the constructed solution by using the Lagrangian coordinates approach. We also consider the density patch problem for the 2D fractional INS equations, and show the global persistence of C 1,γregularity of the density patch boundary when the piecewise jump of density is small enough.2010 Mathematics Subject Classification. Primary 35Q30, 76D05, 35B40. Key words and phrases. fractional inhomogeneous Navier-Stokes equations; maximal regularity; Lagrangian coordinates method; density patch. however, the system (1.2) has additional uniform bounded quantity, that is, the vorticity ω = curl u is uniformly bounded, which makes the L 2 -energy supercritical α < 1 case be globally well-posed.

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Section: Introductionmentioning

confidence: 99%

Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density

Li¹,

Miao²,

Xue³

2021

Preprint

Self Cite

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show abstract

Global well-posedness for 2D fractional inhomogeneous Navier–Stokes equations with rough density

Miao

Xue

2023

Nonlinearity

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This paper is concerned with the global well-posedness issue of the two-dimensional (2D) incompressible inhomogeneous Navier–Stokes equations with fractional dissipation and rough density. By establishing the L t q ( L x p ) -maximal regularity estimate for the generalized Stokes system and using the Lagrangian approach, we prove the global existence and uniqueness of regular solutions for the 2D fractional inhomogeneous Navier–Stokes equations with large velocity field, provided that the initial density is sufficiently close to the constant 1 in L 2 ∩ L ∞ and in the norm of some multiplier spaces. Moreover, we also consider the associated density patch problem, and show the global persistence of C 1 , γ -regularity of the density patch boundary when the piecewise jump of density is small enough.

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Global regularity of density patch for the 3D inhomogeneous Navier–Stokes equations

Cited by 2 publications

References 20 publications

Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density

Global well-posedness for 2D fractional inhomogeneous Navier-Stokes equations with rough density

Global well-posedness for 2D fractional inhomogeneous Navier–Stokes equations with rough density

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