Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations

Shanshan Yang; Hongbiao Jiang; Yinhe Lin

Displaying similar documents to “Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations”

A global existence result for the compressible Navier-Stokes-Poisson equations in three and higher dimensions

Zhensheng Gao, Zhong Tan (2012)

Annales Polonici Mathematici

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The paper is dedicated to the global well-posedness of the barotropic compressible Navier-Stokes-Poisson system in the whole space $ℝ^{N}$ with N ≥ 3. The global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces. The initial velocity has the same critical regularity index as for the incompressible homogeneous Navier-Stokes equations. The proof relies on a uniform estimate for a mixed hyperbolic/parabolic linear system with a convection term. ...

Blow-up for the compressible isentropic Navier-Stokes-Poisson equations

Jianwei Dong, Junhui Zhu, Yanping Wang (2020)

Czechoslovak Mathematical Journal

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We will show the blow-up of smooth solutions to the Cauchy problems for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing and compressible bipolar isentropic Navier-Stokes-Poisson equations in arbitrary dimensions under some restrictions on the initial data. The key of the proof is finding the relations between the physical quantities and establishing some differential inequalities.

Long-Time Asymptotics for the Navier-Stokes Equation in a Two-Dimensional Exterior Domain

Thierry Gallay (2012)

Journées Équations aux dérivées partielles

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We study the long-time behavior of infinite-energy solutions to the incompressible Navier-Stokes equations in a two-dimensional exterior domain, with no-slip boundary conditions. The initial data we consider are finite-energy perturbations of a smooth vortex with small circulation at infinity, but are otherwise arbitrarily large. Using a logarithmic energy estimate and some interpolation arguments, we prove that the solution approaches a self-similar Oseen vortex as $t \to \infty$ . This result was...

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Banach Center Publications

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We give the $L_{p} - L_{q}$ estimate for the Stokes semigroup in a perturbed half-space and some global in time existence theorems for small solutions to the Navier-Stokes equation.

Regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system

Nana Pan, Jishan Fan, Yong Zhou (2021)

Applications of Mathematics

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We prove a regularity criterion for a nonhomogeneous incompressible Ginzburg-Landau-Navier-Stokes system with the Coulomb gauge in $ℝ^{3}$ . It is proved that if the velocity field in the Besov space satisfies some integral property, then the solution keeps its smoothness.

Self-improving bounds for the Navier-Stokes equations

Jean-Yves Chemin, Fabrice Planchon (2012)

Bulletin de la Société Mathématique de France

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We consider regular solutions to the Navier-Stokes equation and provide an extension to the Escauriaza-Seregin-Sverak blow-up criterion in the negative regularity Besov scale, with regularity arbitrarly close to $- 1$ . Our results rely on turning a priori bounds for the solution in negative Besov spaces into bounds in the positive regularity scale.

Regularity criterion for 3D Navier-Stokes equations in terms of the direction of the velocity

Alexis Vasseur (2009)

Applications of Mathematics

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In this short note we give a link between the regularity of the solution $u$ to the 3D Navier-Stokes equation and the behavior of the direction of the velocity $u / | u |$ . It is shown that the control of $Div (u / | u |)$ in a suitable $L_{t}^{p} (L_{x}^{q})$ norm is enough to ensure global regularity. The result is reminiscent of the criterion in terms of the direction of the vorticity, introduced first by Constantin and Fefferman. However, in this case the condition is not on the vorticity but on the velocity itself. The proof, based...

On the Qualitative Behavior of the Solutions to the 2-D Navier-Stokes Equation

M. Pulvirenti (2008)

Bollettino dell'Unione Matematica Italiana

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This talk, based on a research in collaboration with E. Caglioti and F.Rousset, deals with a modified version of the two-dimensional Navier-Stokes equation wich preserves energy and momentum of inertia. Such a new equation is motivated by the occurrence of different dissipation time scales. It is also related to the gradient flow structure of the 2-D Navier-Stokes equation. The hope is to understand intermediate asymptotics.

Global regularity for the 3D inhomogeneous incompressible Navier-Stokes equations with damping

Kwang-Ok Li, Yong-Ho Kim (2023)

Applications of Mathematics

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This paper is concerned with the 3D inhomogeneous incompressible Navier-Stokes equations with damping. We find a range of parameters to guarantee the existence of global strong solutions of the Cauchy problem for large initial velocity and external force as well as prove the uniqueness of the strong solutions. This is an extension of the theorem for the existence and uniqueness of the 3D incompressible Navier-Stokes equations with damping to inhomogeneous viscous incompressible fluids. ...

Long-time behavior for 2D non-autonomous g-Navier-Stokes equations

Cung The Anh, Dao Trong Quyet (2012)

Annales Polonici Mathematici

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We study the first initial boundary value problem for the 2D non-autonomous g-Navier-Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback $_{σ}$ -attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Furthermore, when the force...

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R. H. Dyer, D. E. Edmunds (1971)

Colloquium Mathematicae

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Higher order estimates in further dimensions for the solutions of Navier-Stokes equations

Michael Wiegner (2003)

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Global attractor for the Navier-Stokes equations in a cylindrical pipe

Piotr Kacprzyk (2010)

Annales Polonici Mathematici

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Global existence of regular special solutions to the Navier-Stokes equations describing the motion of an incompressible viscous fluid in a cylindrical pipe has already been shown. In this paper we prove the existence of the global attractor for the Navier-Stokes equations and convergence of the solution to a stationary solution.

Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases

Marzia Bisi, Laurent Desvillettes (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in...

On the stability of compressible Navier-Stokes-Korteweg equations

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Annales Polonici Mathematici

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We consider the compressible Navier-Stokes-Korteweg (N-S-K) equations. Through a remarkable identity, we reveal a relationship between the quantum hydrodynamic system and capillary fluids. Using some interesting inequalities from quantum fluids theory, we prove the stability of weak solutions for the N-S-K equations in the periodic domain $Ω =^{N}$ , when N=2,3.

The Stokes system in the incompressible case-revisited

Rainer Picard (2008)

Banach Center Publications

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The classical Stokes system is reconsidered and reformulated in a functional analytical setting allowing for low regularity of the data and the boundary. In fact the underlying domain can be any non-empty open subset Ω of ℝ³. A suitable solution concept and a corresponding solution theory is developed.

Serrin-type regularity criterion for the Navier-Stokes equations involving one velocity and one vorticity component

Zujin Zhang (2018)

Czechoslovak Mathematical Journal

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We consider the Cauchy problem for the three-dimensional Navier-Stokes equations, and provide an optimal regularity criterion in terms of $u_{3}$ and $ω_{3}$ , which are the third components of the velocity and vorticity, respectively. This gives an affirmative answer to an open problem in the paper by P. Penel, M. Pokorný (2004).

Global solutions, structure of initial data and the Navier-Stokes equations

Piotr Bogusław Mucha (2008)

Banach Center Publications

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In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the L₂-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations. ...

Asymptotic stability of Navier-Stokes flow past an obstacle

Piotr Biler, Marco Cannone, Grzegorz Karch (2004)

Banach Center Publications

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Results on the asymptotic stability of solutions of the exterior Navier-Stokes problem in ℝ³ are proved in the framework of weak $L^{p}$ spaces.

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Piotr Bogusław Mucha (2001)

Colloquium Mathematicae

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An $L_{p}$ -estimate with a constant independent of time for solutions of the linearized compressible Navier-Stokes system in the whole space (under the assumption that solutions have compact supports in space) is obtained.