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Oscillatory solution to semilinear dissipative wave equations

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Chinese Science Bulletin 1998年第9期43卷 787-788页

作者： yin, huicheng Department of Mathematics Nanjing University Nanjing China

Almost global smooth solutions of the 3D quasilinear Klein-Gordon equations on the product space R^(2)×T

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Science China Mathematics 2024年第12期67卷 2713-2752页

作者： Jun Li Fei Tao huicheng yin Department of Mathematics Nanjing UniversityNanjing 210093China School of Mathematical Sciences and Mathematical Institute Nanjing Normal UniversityNanjing 210023China

In this paper,for the 3D quadratic nonlinear Klein-Gordon equation on the product space R^(2)×T,we focus on the lower bound of the lifespan of the smooth solution with slowly decaying initial *** the size of initial data is bounded by ε_(0)>0,it is shown that a smooth solution exists up to the time C_(0)/20 with0 being sufficiently small and e^(c0)/ε_(0)^(2)>0 being some suitable *** that the solution of the corresponding 3D linear homogeneous Klein-Gordon equation on R^(2)×T only admits the optimal time-decay rate(1+t)−1,from which we generally derive the lifespan of the nonlinear Klein-Gordon equation up to e^(c0/ε0)rather than the more precise e^(c0/ε^(2)0) here.

关键词： quasilinear Klein-Gordon equation almost global solution Z-norm Littlewood-Paley decomposition space-time resonance method energy estimate

On the nonexistence of a global nontrivial subsonic solution in a 3D unbounded angular domain

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Science China Mathematics 2010年第7期53卷 1750-1763页

作者： Li Jun yin huicheng Zhou ChunHui Nanjing Univ Dept Math & IMS Nanjing 210093 Peoples R China

In this paper, under some assumptions on the flow with a low Mach number, we study the nonexistence of a global nontrivial subsonic solution in an unbounded domain Ω which is one part of a 3D ramp. The flow is assumed to be steady, isentropic and irrotational, namely, the movement of the flow is described by the potential equation. By establishing a fundamental a priori estimate on the solution of a second order linear elliptic equation in Ω with Neumann boundary conditions on Ω and Dirichlet boundary value at some point of Ω, we show that there is no global nontrivial subsonic flow with a low Mach number in such a domain Ω.

关键词： subsonic flow potential equation modified Bessel functions weighted Hlder space

ON THE SINGULARITIES OF SOLUTIONS TO 4-D SEMILINEAR DISPERSIVE WAVE EQUATIONS

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Analysis in Theory and Applications 2005年第2期21卷 176-187页

作者： Ning Xu huicheng yin Nanjing University and PLA Nanjing Institute of Politics China Nanjing University China

In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz＇s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal

关键词： Dispersive wave equation tangent vector fields Strichartz's inequality pseudodifferential operator

On Compressible Smooth Viscous Fluids in Slowly Expanding Balls

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Analysis in Theory and Applications 2019年第1期35卷 28-65页

作者： huicheng yin Lin Zhang School of Mathematical Sciences Jiangsu Provincial Key Laboratory for Numerical Simulation of Large Scale Complex Systems Nanjing Normal University

In[17]and[19,20],the global existence and large time behaviors of smooth compressible fluids(including inviscid gases of Euler equations,viscous gases of Navier-Stokes equations,and rarified gases of Boltzmann equation,respectively)have been established in an infinitely expanding ball with a constant expansion *** paper concerns with the viscous fluids in a slowly expanding *** involved analy-sis on the density function and the weighted energy estimates,we show that the fluid in the slowly expanding ball smoothly tends to a vacuum state and there is no appearance of vacuum in any part of the expansive *** present result is a meaningful supplement to the one in[19].

关键词： Compressible Navier-Stokes equations slowly expanding ball weighted energy estimate global existence

The Lifespan for 3-D Spherically Symmetric Compressible Euler Equations

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Acta Mathematica Sinica,English Series 1998年第4期14卷 527-534页

作者： yin huicheng Qiu Qingjiu, Department of Mathematics, Nanjing University, Nanjing 210093, China Department of Mathematics Nanjing University Nanjing China

In this paper, we study the lifespan of solutions for three dimensional compressible Euler equations with spherically symmetric initial data that is a small perturbation of amplitude ε from a constant state. From our... 详细信息

关键词： Lifespan Compressible Euler equation

THE BLOWUP OF RADIALLY SYMMETRIC SOLUTIONS FOR 2-D QUASILINEAR WAVEEQUATIONS WITH CUBIC NONLINEARITY

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Chinese Annals of Mathematics,Series B 1999年第4期20卷 455-472页

作者： yin huicheng ZHENG QIN(Department of Mathematics, Nanjing University Nanjing 210093, China) Department of Mathematics Nanjing University Nanjing 210093 China

For a special class of quasilinear wave equations with small initial data which satisfy the nondegenerate assumption, the authors prove that the radially symmetric solution develops singularities in the second order derivatives in finite time while the first order derivatives and the solution itself remain continuous and small. More precisely, it turns out that this solution is a "geometric blowup solution of cusp type", according to the terminology posed by S. Alinhac[2].

关键词： Lifespan Geometric blowup Nash-M■ser iteration

Preface Special Issue Dedicated to Professor Weiyi Su's 80th Birthday

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Analysis in Theory and Applications 2020年第3期36卷 233-234页

作者： Yongzhong Sun huicheng yin Ping Zhang Nanjing University Chinese Academy of Sciences

This special issue is dedicated to Professor Weiyi Su for the celebration of her 80th birthday and for honoring her more than 50 years’ research and education career in *** Su was born in Yichang, Hubei Province, China in 1938. She joined the Department of Mathematics of Nanjing University (NJU) as an assistant professor after her five-year undergraduate study there from 1956 to 1961.

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THE UNIQUENESS OF A TRANSONIC SHOCK IN A NOZZLE FOR THE 2-D COMPLETE EULER SYSTEM WITH THE VARIABLE END PRESSURE

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Journal of Partial Differential Equations 2008年第3期21卷 263-288页

作者： Cui Dacheng yin huicheng Department of Mathematics & IMS Nanjing University Nanjing 210093 China

In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especially, we remove the crucial but unnatural assumption in recent references which the transonic shock must be assumed to go through a fixed point in advance.

关键词： Steady Euler system supersonic flow subsonic flow transonic shock nozzle.