Existence and smoothness of a class of Burgers equations
Partial Differential Equations in Applied Mathematics, 2021 In this paper we consider a class of Burgers equations. We propose a new method for investigation for existence of classical solutions.
Svetlin G. Georgiev, Gal Davidi
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Global Existence for the Multi-Dimensional Compressible Viscoelastic flows [PDF]
, 2010 The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces.
Hu, Xianpeng, Wang, Dehua
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Global existence for quasilinear wave equations close to Schwarzschild [PDF]
Communications in Partial Differential Equations, 2016 In this article, we study the quasilinear wave equation where the metric is close (and asymptotically equal) to the Schwarzschild metric . Under suitable assumptions of the metric coefficients, and assuming that the initial data for u is small enough, we
Hans Lindblad, M. Tohaneanu
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Global Existence for Capillary Water Waves [PDF]
Communications on Pure and Applied Mathematics, 2014 Consider the capillary water waves equations, set in the whole space with infinite depth, and consider small data (i.e., sufficiently close to zero velocity, and constant height of the water). We prove global existence and scattering. The proof combines in a novel way the energy method with a cascade of energy estimates, the space‐time resonance method
Jalal Shatah +2 more
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On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping [PDF]
, 2016 In this paper, we are concerned with the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping {∂tρ+div (ρu)=0,∂t(ρu)+div (ρu⊗u+pId)=−α(t)ρu,ρ(0,x)=ρ¯+ερ0(x),u(0,x)=εu0(x), where
Fei Hou, Huicheng Yin
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Uniform boundedness and extinction results of solutions to a predator–prey system
Electronic Journal of Qualitative Theory of Differential Equations, 2020 Global existence, positivity, uniform boundedness and extinction results of solutions to a system of reaction-diffusion equations on unbounded domain modeling two species on a predator–prey relationship is considered.
Mokhtar Kirane +2 more
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Asymptotic behavior of solutions for linear evolutionary boundary value problem of viscoelastic damped wave equation [PDF]
Mathematica Bohemica, 2020 We study the existence of global in time and uniform decay of weak solutions to the initial-boundary value problem related to the dynamic behavior of evolution equation accounting for rotational inertial forces along with a linear nonlocal frictional ...
Mohamed Berbiche
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Existence of a Global Solution for a Viscoelastic System
Journal of Mathematical Analysis and Applications, 1998 AbstractIn this paper, a unique classical solution (v,u) of the Cauchy problem (1), (2) is obtained if |v0(x)|1+α≤M, |u0(x)|2+α≤M. The a priori estimates |v(x,t)|1+α, |u(x,t)|2+α≤M(T) are obtained by using the maximum principle without the restriction lim|x|→±∞(v0(x),u0(x))=(v±,u±), wherev±,u±are constants. This resolves a problem proposed by J.
Yun‐guang Lu
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On Global Well-Posedness of the Lagrangian Averaged Euler Equations [PDF]
, 2006 We study the global well-posedness of the Lagrangian averaged Euler equations in three dimensions. We show that a necessary and sufficient condition for the global existence is that the bounded mean oscillation of the stream function is integrable in ...
Hou, Thomas Y., Li, Congming
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Global Existence for the Confined Muskat Problem [PDF]
SIAM Journal on Mathematical Analysis, 2014 29 pages, 1 ...
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