Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum

Silva, Pablo Braz e; Cruz, F.W.; Rojas-Medar, Marko Antonio; Santos, Élcio Gonçalves dos

doi:10.1016/j.jmaa.2018.12.075

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…Here, let us recall that, for the 3-D case, under certain assumptions, Lukaszewicz [25] established the existence of weak solutions for a short time by using linearization and an almost fixed point theorem. Braz e Silva and collaborators in [4,5] constructed the existence of global in time weak solutions of system (1.1) when the initial density is not necessarily strictly positive. Local wellposedness of strong solution to system (1.1) was constructed by Lukaszewicz [25] when the initial density is strictly separated from zero.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The unique global solvability of a nonhomogeneous incompressible asymmetric fluids in two and three dimensions

Zhang

Qiao

2022

Preprint

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The present paper studies the nonhomogeneous incompressible asymmetric fluids in two and three dimensions. The main aim is to obtain the unique global solvability of the system with only bounded nonnegative initial density. More precisely, we construct the global existence of the solution with large data in 2-D and the existence of local in time solution for arbitrary large data and global in time for some smallness conditions in 3-D. In addition, the uniqueness of the solution is proved under quite soft assumptions about its regularity through a Lagrangian approach. These conclusions can be viewed as a generalization of the one established by [ P. Braz e Silva, F. Cruz, M. Loayza and M. Rojas-Medar, J. Differential Equations, 269 (2020), pp. 1319–1348], which does not allow the presence of initial vacuum.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

The unique global solvability of a nonhomogeneous incompressible asymmetric fluids in two and three dimensions

Zhang

Qiao

2022

Preprint

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“…Recently, in a bounded domain Ω, removed the compatibility condition, Li [23] proved the local existence and uniqueness of strong solutions to the 3-D nonhomogeneous Navier-Stokes equations for any initial Concerning the model considered in this paper, let us recall that, for the 3-D case, under certain assumptions, Lukaszewicz [25] established the existence of weak solutions for a short time by using linearization and an almost fixed point theorem. Braz e Silva and collaborators in [4,5] constructed the existence of global in time weak solutions of system (1.1) when the initial density is not necessarily strictly positive. Local existence of strong solutions to system (1.1) was constructed by Lukaszewicz [25] when the initial density is strictly separated from zero.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The unique global solvability of the nonhomogeneous incompressible asymmetric fluids with vacuum

Xu¹,

Zhang²,

Qiao³

2020

Preprint

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The present paper deals with the nonhomogeneous incompressible asymmetric fluids equations in dimension d = 2, 3. The aim is to prove the unique global solvability of the system with only bounded nonnegative initial density and H 1 initial velocities. We first construct the global existence of the solution with large data in 2-D. Next, we establish the existence of local in time solution for arbitrary large data and global in time for some smallness conditions in 3-D. Finally, the uniqueness of the solution is proved under quite soft assumptions about its regularity through a Lagrangian approach. In particular, the initial vacuum is allowed.

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“…On the other hand, for the initial density allowing vacuum states, Lukaszewicz [18] (see also [19,Chapter 3]) obtained short-time existence of weak solutions provided that the initial functions u 0 and w 0 are in H 1 0 and that the initial density ρ 0 is uniformly bounded and satisfies ρ −1 0 L 3 < ∞, while Braz e Silva and Santos [12] established the global existence of weak solutions. In [10], under smallness assumptions on the initial data, weak solutions with improved regularity were obtained. At the same time, imposing a compatibility condition on the initial data, Zhang and Zhu [26] showed the global existence of strong solution with nonnegative density in R 3 under some smallness condition.…”

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confidence: 99%

Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

Zhong¹

2022

CPAA

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<p style='text-indent:20px;'>We consider an initial boundary value problem of three-dimensional (3D) nonhomogeneous magneto-micropolar fluid equations in a bounded simply connected smooth domain with homogeneous Dirichlet boundary conditions for the velocity and micro-rotational velocity and Navier-slip boundary condition for the magnetic field. We prove the global existence and exponential decay of strong solutions provided that some smallness condition holds true. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time weighted techniques.</p>

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Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum

Cited by 11 publications

References 17 publications

The unique global solvability of a nonhomogeneous incompressible asymmetric fluids in two and three dimensions

The unique global solvability of a nonhomogeneous incompressible asymmetric fluids in two and three dimensions

The unique global solvability of the nonhomogeneous incompressible asymmetric fluids with vacuum

Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

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