Local strong solution for a class of non-Newtonian fluids with heat-conducting and state function

2019 ◽  
Vol 60 (9) ◽  
pp. 091503
Author(s):  
Yunliang Zhang ◽  
Zhidong Guo
Keyword(s):  
Strong Solution ◽  
Newtonian Fluids ◽  
State Function ◽  
Heat Conducting ◽  
Local Strong Solution

scholarly journals Local Strong Solution for a Class of Shear Thickening Fluids with Non-Newtonian Potential and Heat-Conducting

2015 ◽  
Vol 2015 ◽  
pp. 1-17
Author(s):  
Yunliang Zhang ◽  
Zhidong Guo
Keyword(s):  
Existence And Uniqueness ◽  
Shear Thickening ◽  
Strong Solutions ◽  
Newtonian Potential ◽  
State Function ◽  
Heat Conducting ◽  
Strong Nonlinearity ◽  
Shear Thickening Fluids ◽  
Local Strong Solutions ◽  
Local Strong Solution

The aim of this paper is to discuss the model for a class of shear thickening fluids with non-Newtonian potential and heat-conducting. Existence and uniqueness of local strong solutions for the model are proved. In this paper, there exist two difficulties we have to overcome. One is the strong nonlinearity of the system. The other is that the state function is not fixed.

scholarly journals Local strong solution for the incompressible Korteweg model

2006 ◽  
Vol 342 (3) ◽  
pp. 169-174 ◽  
Author(s):  
Mamadou Sy ◽  
Didier Bresch ◽  
Francisco Guillén-González ◽  
Jérôme Lemoine ◽  
Maria Angeles Rodríguez-Bellido
Keyword(s):  
Strong Solution ◽  
Local Strong Solution

scholarly journals Solutions and Drift Homogenization for a Class of Viscous Lake Equations in

2021 ◽  
Author(s):  
Maoting Tong
Keyword(s):  
Continuous Function ◽  
Strong Solution ◽  
Initial Value Problem ◽  
Smooth Function ◽  
Three Dimensional ◽  
Usual Sense ◽  
Bounded Operators ◽  
Initial Value ◽  
Lake Equations ◽  
Local Strong Solution

In this paper we study solutions and drift homogenization for a class of viscous lake equations by using the method of semigroups of bounded operators. Suppose that the initial value i.e.,for some Hölder continuous function onwith smooth function value satisfying and Then the initial value problem (2) for viscous lake equations has a unique smooth local strong solution. Using this result we study the drift homogenization for three-dimensional stationary Stokes equation in the usual sense

scholarly journals The Keller–Segel system on bounded convex domains in critical spaces

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Matthias Hieber ◽  
Klaus Kress ◽  
Christian Stinner
Keyword(s):  
Periodic Solution ◽  
Initial Data ◽  
Strong Solution ◽  
Convex Domains ◽  
Critical Spaces ◽  
Bounded Convex Domain ◽  
Local Strong Solution ◽  
Time Periodic ◽  
Bounded Convex ◽  
Time Periodic Solution

AbstractConsider the classical Keller–Segel system on a bounded convex domain $$\varOmega \subset {\mathbb {R}}^3$$ Ω ⊂ R 3 . In contrast to previous works it is not assumed that the boundary of $$\varOmega $$ Ω is smooth. It is shown that this system admits a local, strong solution for initial data in critical spaces which extends to a global one provided the data are small enough in this critical norm. Furthermore, it is shown that this system admits for given T-periodic and sufficiently small forcing functions a unique, strong T-time periodic solution.

Global strong solution for viscous incompressible heat conducting Navier–Stokes flows with density-dependent viscosity

2018 ◽  
Vol 16 (05) ◽  
pp. 623-647 ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Strong Solution ◽  
Variable Viscosity ◽  
Initial Density ◽  
Energy Estimates ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Stokes Flows ◽  
Global Strong Solution ◽  
Regularity Properties ◽  
Nonhomogeneous Heat

We study an initial boundary value problem for the nonhomogeneous heat conducting fluids with non-negative density. First of all, we show that for the initial density allowing vacuum, the strong solution exists globally if the gradient of viscosity satisfies [Formula: see text]. Then, under certain smallness condition, we prove that there exists a unique global strong solution to the 2D viscous nonhomogeneous heat conducting Navier–Stokes flows with variable viscosity. Our method relies upon the delicate energy estimates and regularity properties of Stokes system and elliptic equation.

Sign in / Sign up

Export Citation Format

Share Document