scholarly journals Global existence of solutions of the spherically symmetric Vlasov-Einstein system with small initial data

1996 ◽  
Vol 176 (2) ◽  
pp. 475-478 ◽  
Author(s):  
G. Rein ◽  
A. D. Rendall
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Existence Of Solutions ◽  
Spherically Symmetric ◽  
Small Initial Data ◽  
Global Existence Of Solutions

scholarly journals Global Existence of Solutions to a Class of Reaction–Diffusion Systems on Rn

2021 ◽  
Author(s):  
Salah Badraoui
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Classical Solution ◽  
Space Dimension ◽  
Existence Of Solutions ◽  
Bounded Function ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems

We prove in this work the existence of a unique global nonnegative classical solution to the class of reaction–diffusion systems uttx=aΔutx−guvm,vttx=dΔvtx+λtxguvm, where a>0, d>0, t>0,x∈Rn, n,m∈N∗, λ is a nonnegative bounded function with λt.∈BUCRn for all t∈R+, the initial data u0, v0∈BUCRn, g:BUCRn→BUCRn is a of class C1,dgudu∈L∞R, g0=0 and gu≥0 for all u≥0. The ideas of the proof is inspired from the work of Collet and Xin who proved the same result in the particular case d>a=1, λ=1,gu=u. Moreover, they showed that the L∞-norm of v can not grow faster than Olnlnt for any space dimension.

scholarly journals Well-Posedness of the Two-Dimensional Fractional Quasigeostrophic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yongqiang Xu
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Sobolev Spaces ◽  
Existence Of Solutions ◽  
Local Existence ◽  
Well Posedness ◽  
Two Dimensional ◽  
Small Initial Data ◽  
General Initial Data ◽  
Local Existence Of Solutions

This paper is concerned with the fractional quasigeostrophic equation with modified dissipativity. We prove the local existence of solutions in Sobolev spaces for the general initial data and the global existence for the small initial data when1/2≤α<1.

Generalized Invariant Sets for the Boltzmann Equation

1997 ◽  
Vol 07 (04) ◽  
pp. 457-476 ◽  
Author(s):  
T. Goudon
Keyword(s):  
Boltzmann Equation ◽  
Initial Data ◽  
Global Existence ◽  
Existence Of Solutions ◽  
Invariant Set ◽  
Invariant Sets ◽  
Soft Or ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
The Boltzmann Equation

We are interested in the initial value problem for the Boltzmann equation, when the initial data u0 belongs to a set B0 = {δ0m1 (0,x,v) ≤ u0(x,v) ≤ C0m2 (0,x,v)} where m1, m2 are traveling Maxwellians. We consider soft or Maxwell's interactions with cutoff (7/3 < s ≤ 5) and C0 smaller than a bound depending on the coefficients of m2. We obtain global existence of solutions remaining in a "generalized invariant set" Bt ⊂ B∞, characterized by these particular states.

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