In mathematics, the viscosity solution concept was introduced in the early 1980s by Pierre-Louis Lions and Michael G. Crandall as a generalization of the...

prestigious Fields Medal. He was cited for his contributions to viscosity solutions, the Boltzmann equation, and the calculus of variations. He has also...

Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another...

classical solutions only for a sufficiently smooth value function, which is not guaranteed in most situations. Instead, the notion of a viscosity solution is...

Hamilton–Jacobi equation, there is a very different definition of weak solution called viscosity solution. Evans, L. C. (1998). Partial Differential Equations. Providence:...

Intrinsic viscosity [ η ] {\displaystyle \left[\eta \right]} is a measure of a solute's contribution to the viscosity η {\displaystyle \eta } of a solution. If...

derivative with respect to time. The value function is the unique viscosity solution to the Hamilton–Jacobi–Bellman equation. In an online closed-loop...

limiting value is the intrinsic viscosity, which is a good measure of the polymerization degree. "Dilute Solution Viscosity of Polymers". "IUPAC". doi:10...

Relative viscosity ( η r e l {\displaystyle \eta _{rel}} ) (a synonym of "viscosity ratio") is the ratio of the viscosity of a solution ( η {\displaystyle...

obtained solutions in 1910 for fluids with viscosity but without heat conductivity and for fluids with heat conductivity but without viscosity. Following...

(/daɪˈleɪtənt/, /dɪ-/) (also termed shear thickening) material is one in which viscosity increases with the rate of shear strain. Such a shear thickening fluid...

up to 30% mass percentage, after which viscosity increases). The increase in viscosity for sucrose solutions is particularly dramatic, and explains in...

not follow Newton's law of viscosity, that is, it has variable viscosity dependent on stress. In particular, the viscosity of non-Newtonian fluids can...

made significant contributions to the development of the theory of viscosity solutions of nonlinear equations, to the understanding of the Hamilton–Jacobi–Bellman...

natural skin oils. Concentrated (50%) aqueous solutions of sodium hydroxide have a characteristic viscosity, 78 mPa·s, that is much greater than that of...

arbitrary constants. This solution is valid in the domain r ≥ 1 and for A < −2ν. In Cartesian coordinates, when the viscosity is zero (ν = 0), this is:...

equations; asymptotic analysis of Ginzburg-Landau type systems, viscosity solutions, and mathematical finance. Currently he is working on mean field...

Moreover, the viscosity of the reaction mixture is reduced, preventing autoacceleration at high monomer concentrations. A decrease in viscosity of the reaction...

capillary based method of measuring viscosity. It is recommended for higher viscosity cellulosic polymer solutions. The advantage of this instrument is...

elastic fluids exhibit shear thinning (viscosity decreases as shear strain is applied), because they are solutions containing polymers. But Boger fluids...

properties play significant roles in disease processes. Blood viscosity is determined by plasma viscosity, hematocrit (volume fraction of red blood cell, which...

the flow of liquids is viscosity. Intuitively, viscosity describes the resistance of a liquid to flow. More technically, viscosity measures the resistance...

techniques are necessary to prove this. This led to the development of viscosity solutions in the 1980s by Pierre-Louis Lions and Michael G. Crandall, and Lions...

describe the viscous stress and the strain rate are related by a constant viscosity tensor that does not depend on the stress state and velocity of the flow...

equation. Poiseuille's equation describes the pressure drop due to the viscosity of the fluid; other types of pressure drops may still occur in a fluid...

This equation represents apparent viscosity where apparent viscosity is the shear stress divided by shear rate. Viscosity is dependent on stress. This is...

Kaminsky M (1957). "Ion-solvent interaction and the viscosity of strong-electrolyte solutions". Discussions of the Faraday Society. 24: 171. doi:10...

H-principle Atiyah–Singer index theorem Bäcklund transform Viscosity solution Weak solution Loewy decomposition of linear differential equations Broer–Kaup...

transition, the yield temperature, and the viscosity of a melt. An understanding of the thermodynamics of a polymer solution is critical to prediction of its behavior...

Fleming, W.; Soner, M. (2006). Controlled Markov Processes and Viscosity Solutions. Springer. Stein, J. L. (2012). Stochastic Optimal Control and the...