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袁源副研究员：Blowup of the entropy-bounded classical solutions to the nonisentropic compressible Navier-Stokes equations
非等熵 可压缩 纳维-斯托克斯方程 熵界经典解 爆炸
2023/4/11
This talk concerns the instantaneous blowup of entropy-bounded classical solutions to the vacuum free boundary problem or the Cauchy problem of nonisentropic compressible Navier-Stokes equations.
Global classical solutions for partially dissipative hyperbolic system of balance laws
balance laws entropy dissipative classical solutions Chemin-Lerner’s spaces
2012/2/29
This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a gener...
Global Classical Solutions of the Relativistic Vlasov-Darwin System with Small Cauchy Data: the Generalized Variables Approach
Vlasov-Darwin Cauchy Problem Global Classical Solutions
2011/8/25
Abstract: We show that a smooth, small enough Cauchy datum launches a unique classical solution of the relativistic Vlasov-Darwin (RVD) system globally in time. A similar result is claimed in Comm. Ma...
On the uniqueness of classical solutions of Cauchy problems
Cauchy problem a necessary and sufficient condition for unique-ness European call-type options Strict local martingales
2010/11/2
Given that the terminal condition is of at most linear growth, it is well known that a Cauchy problem admits a unique classical solution when the coefficient multiplying the second
derivative is also...
Lifespan of Classical Solutions to Quasi-linear Hyperbolic Systems with Small BV Normal Initial Data
Quasi-linear hyperbolic system Weakly linear degeneracy Matching condition Normalized Coordinates Blow-up Lifespan.
2018/4/20
In this paper, we first give a lower bound of the lifespan and some estimates of classical solutions to the Cauchy problem for general quasi-linear hyperbolic systems, whose characteristic fields are ...
Global Classical Solutions to the Equations of Two-Dimensional MHD Transverse Flow
MHD transverse flow global classical solution
2007/12/11
A new method for constructing the symmetric form for the hyperbolic systems is introduced. Then a new symmetric form of the equations of MHD transverse flow is constructed by adding an additional equa...
GLOBAL CLASSICAL SOLUTIONS AND EXPLICITEXACT SOLUTIONS TO A KIND OF QUASILINEARPARTIAL DIFFERENTIAL EQUATIONS
Quasilinear equation the Cauchy problem
2007/8/7
In this paper the authors give a complete result on the global existence andthe lifesspan of classical solutions to the Cauchy problem for a kind 0f quasilillear partial differelitial equations of phy...