Vanishing viscosity for non-homogeneous asymmetric fluids in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>: The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math> case

Silva, Pablo Braz e; Cruz, F.W.; Rojas-Medar, Marko Antonio

doi:10.1016/j.jmaa.2014.05.060

Cited by 14 publications

(5 citation statements)

References 14 publications

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“…Concerning the model considered in this paper, P. Braz e Silva and E. G. Santos established in the existence of global in time weak solutions with initial density not necessarily strictly positive. The vanishing viscosity problem for variable density asymmetric incompressible fluids was studied by P. Braz e Silva, F. W. Cruz, and M. A. Rojas‐Medar in for the L 2 context and by P. Braz e Silva, E. Fernández‐Cara, and M. A. Rojas‐Medar in for the L p context, p > 3(see for the homogeneous case). Through a spectral semi‐Galerkin method, J. L. Boldrini, M. A. Rojas‐Medar, and E. Fernández‐Cara proved in the existence and uniqueness of a strong solution (local and global in time) in bounded domains in

{double-struckR}^{3}

with regular boundary.…”

Section: Introductionmentioning

confidence: 99%

Semi‐strong and strong solutions for variable density asymmetric fluids in unbounded domains

Silva

Cruz

Rojas-Medar

2016

Math Methods in App Sciences

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We establish the existence of local in time semi‐strong solutions and global in time strong solutions for the system of equations describing flows of viscous and incompressible asymmetric fluids with variable density in general three‐dimensional domains with boundary uniformly of class C3. Under suitable assumptions, uniqueness of local semi‐strong solutions is also proved. Copyright © 2016 John Wiley & Sons, Ltd.

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{double-struckR}^{3}

with regular boundary.…”

Section: Introductionmentioning

confidence: 99%

Semi‐strong and strong solutions for variable density asymmetric fluids in unbounded domains

Silva

Cruz

Rojas-Medar

2016

Math Methods in App Sciences

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“…Later on, Ye [24] improved their result by removing the compatibility condition and furthermore obtained exponential decay of strong solution (see also [23] for the case of bounded domains). There are other interesting studies on the nonhomogeneous micropolar fluid equations, such as the vanishing viscosity problem [7,11], error estimates for spectral semi-Galerkin approximations [13], the local existence of semi-strong solutions [8], and strong solutions in thin domains [9].…”

mentioning

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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“…Applying the Desjardins interpolation inequality, Liu and Zhong [17] investigated the global existence and exponential decay of strong solution to the 2D initial boundary value problem with general large data and vacuum. There are also other interesting studies on the nonhomogeneous micropolar fluid equations, such as the vanishing viscosity problem [3,7], error estimates for spectral semi-Galerkin approximations [11], the local existence of semi-strong solutions [4], and strong solutions in thin domains [5]. Recently, by spatial-weighted energy method, Zhong [26] proved the local existence of strong solutions to the Cauchy problem of (1.2) in R 2 .…”

mentioning

confidence: 99%

Global strong solution to the nonhomogeneous micropolar fluid equations with large initial data and vacuum

Zhong

2022

DCDS-B

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<p style='text-indent:20px;'>We study the Cauchy problem of nonhomogeneous micropolar fluid equations with zero density at infinity in the whole plane <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula>. We derive the global existence and uniqueness of strong solutions if the initial density decays not too slowly at infinity. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies upon the delicate weighted energy estimates and the structural characteristics of the system under consideration.</p>

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Vanishing viscosity for non-homogeneous asymmetric fluids in R3: The L2 case

Cited by 14 publications

References 14 publications

Semi‐strong and strong solutions for variable density asymmetric fluids in unbounded domains

Semi‐strong and strong solutions for variable density asymmetric fluids in unbounded domains

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

Global strong solution to the nonhomogeneous micropolar fluid equations with large initial data and vacuum

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