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Around 3D Boltzmann non linear operator without angular cutoff, a new formulation

Radjesvarane Alexandre (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose a new formulation of the 3D Boltzmann non linear operator, without assuming Grad's angular cutoff hypothesis, and for intermolecular laws behaving as 1/rs, with s> 2. It involves natural pseudo differential operators, under a form which is analogous to the Landau operator. It may be used in the study of the associated equations, and more precisely in the non homogeneous framework.

Asymptotic analysis for a nonlinear parabolic equation on

Eva Fašangová (1998)

Commentationes Mathematicae Universitatis Carolinae

We show that nonnegative solutions of u t - u x x + f ( u ) = 0 , x , t > 0 , u = α u ¯ , x , t = 0 , supp u ¯ compact either converge to zero, blow up in L 2 -norm, or converge to the ground state when t , where the latter case is a threshold phenomenon when α > 0 varies. The proof is based on the fact that any bounded trajectory converges to a stationary solution. The function f is typically nonlinear but has a sublinear growth at infinity. We also show that for superlinear f it can happen that solutions converge to zero for any α > 0 , provided supp u ¯ is sufficiently small.

Asymptotic behavior of a sixth-order Cahn-Hilliard system

Alain Miranville (2014)

Open Mathematics

Our aim in this paper is to study the asymptotic behavior, in terms of finite-dimensional attractors, of a sixth-order Cahn-Hilliard system. This system is based on a modification of the Ginzburg-Landau free energy proposed in [Torabi S., Lowengrub J., Voigt A., Wise S., A new phase-field model for strongly anisotropic systems, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 2009, 465(2105), 1337–1359], assuming isotropy.

Asymptotic behavior of small-data solutions to a Keller-Segel-Navier-Stokes system with indirect signal production

Lu Yang, Xi Liu, Zhibo Hou (2023)

Czechoslovak Mathematical Journal

We consider the Keller-Segel-Navier-Stokes system n t + 𝐮 · n = Δ n - · ( n v ) , x Ω , t > 0 , v t + 𝐮 · v = Δ v - v + w , x Ω , t > 0 , w t + 𝐮 · w = Δ w - w + n , x Ω , t > 0 , 𝐮 t + ( 𝐮 · ) 𝐮 = Δ 𝐮 + P + n φ , · 𝐮 = 0 , x Ω , t > 0 , which is considered in bounded domain Ω N ( N { 2 , 3 } ...

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