Global and blow up solutions to cross diffusion systems
Advances in Nonlinear Analysis, 2015 Necessary and sufficient conditions for global existence of classical solutions to a class of cross diffusion systems on n-dimensional domains are given. Examples of blow up solutions are also presented.
Ahmad Shair, Le Dung
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Nonexistence of traveling waves for a nonlocal Gross-Pitaevskii equation [PDF]
arXiv, 2011 We consider a Gross-Pitaevskii equation with a nonlocal interaction potential. We provide sufficient conditions on the potential such that there exists a range of speeds in which nontrivial traveling waves do not ...
arxiv
$C^{1,α}$-Regularity of energy minimizing maps from a 2-dimentional domain into a Finsler space [PDF]
arXiv, 2011 We show $C^{1,\alpha}$-regularity for energy minimizing maps from a 2-dimensional Riemannian manifold into a Finsler space $(\R^n, F)$ with a Finsler structure $F(u,X)$.
arxiv
Maximal Lp -Lq regularity to the Stokes problem with Navier boundary conditions
Advances in Nonlinear Analysis, 2017 We prove in this paper some results on the complex and fractional powers of the Stokes operator with slip frictionless boundary conditions involving the stress tensor.
Al Baba Hind
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The p-Laplacian with respect to measures [PDF]
arXiv, 2011 We introduce a definition for the $p$-Laplace operator on positive and finite Borel measures that satisfy an Adams-type embedding condition.
arxiv
Nonautonomous Kolmogorov equations in the whole space: a survey on recent results [PDF]
arXiv, 2012 In this paper we survey some recent results concerned with nonautonomous Kolmogorov elliptic operators.
arxiv
Regularity and reduction to a Hamilton-Jacobi equation for a MHD Eyring-Powell fluid
Alexandria Engineering Journal, 2022 The flow under an Eyring-Powell description has attracted interest to model different scenarios related with non-Newtonian fluids. The goal of the present study is to provide analysis of solutions to a one-dimensional Eyring-Powell fluid in ...
José Luis Díaz Palencia +2 more
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Boundary De Giorgi-Ladyzhenskaya classes and their application to regularity of swirl of Navier-Stokes [PDF]
arXiv, 2012 The embeddings theorem of space-boundary-type DeGiorgi-Ladyzhenskaya parabolic classes into Holder spaces is presented, which is useful for regularity considerations for parabolic boundary value problems. Additionaly, the application of this theory to Navier-Stokes-s swirl is presented.
arxiv
Regularity of weak solutions to the 3D stationary tropical climate model
Open MathematicsThis article studies the regularity of weak solutions to the 3D stationary tropical climate model. We prove that when (U,V,θ)\left(U,V,\theta ) belongs to the homogeneous Morrey space M˙2,p(R3){\dot{M}}^{2,p}\left({{\mathbb{R}}}^{3}) with p>3p\gt 3, then
Song Huiyang, Bie Qunyi, Zhou Yanping
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Time-interior gradient estimates for quasilinear parabolic equations [PDF]
Indiana University Mathematics Journal 58 (2009) 351--380, 2013 Bounded smooth solutions of the Dirichlet and Neumann problems for a wide variety of quasilinear parabolic equations, including graphical anisotropic mean curvature flows, have gradient bounded in terms of oscillation and elapsed time.
arxiv