Chengbo Wang (王成波)
Assistant Professor

Mailing Address:

Department of Mathematics
Johns Hopkins University
Baltimore, MD 21218

Office: 222 Krieger Hall
Phone: 410-516-5132
Email:  wangcbo@jhu.edu


 
Research | CV | Teaching | Publications | Some Links

Research Interests :

My research area is in partial differential equations and harmonic analysis.

Much of my research focuses on the study of the Strichartz estimates and their various generalizations for the linear
wave/Schroedinger equation. As applications, we consider also the local and global theory of nonlinear equations
with low regularity.

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Here is my Curriculum Vitae.

Teaching :

Fall 2009:     110.302---Differential Equations with Applications

Spring 2009: 110.417---Partial Differential Equations for Applications

Spring 2009: 110.726---Topics in Analysis

Fall 2008:     110.443---Fourier Analysis

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Publications and Preprints :

         We obtain KSS, Strichartz and certain weighted Strichartz estimate for the wave equation on (R^d, g),
         d \geq 3, when metric g is non-trapping and approaches the Euclidean metric like x ^{- r} with r>0.
         Using the KSS estimate, we prove almost global existence for quadratically semilinear wave equations with
         small initial data for r> 1 and d=3. Also, we establish the Strauss conjecture when the metric is radial with
         r>1 for d= 3.

       In this paper, we establish an optimal dual version of trace estimate involving angular regularity. Based on
         this estimate, we get the generalized Morawetz estimates and weighted Strichartz estimates for the solutions
         to a large class of evolution equations, including the wave and Schroedinger equation. As applications of these
         estimates, we prove the Strauss' conjecture with a kind of mild rough data for 2\leq n \leq 4, and a result of
         global well-posedness with small data for the nonlinear Schroedinger equation.

         In this paper, we study the ill-posdness of the Cauchy problem for semilinear wave equation with very low
         regularity, where the nonlinear term depends on $u$ and $\partial_t u$. We prove a ill-posedness result for
         the ``defocusing" case, and give an alternative proof for the supercritical ``focusing" case, which improves
         our previous result (Chin. Ann. Math. Ser. B 26(3), 361--378, 2005).

        In this paper, we give several remarks on Strichartz estimates for homogeneous wave equation. In particular,
         we show that the endpoint $L^4_t L^\infty_x$ estimate fail to be hold for $n=2$ in general. When the data
         is radial, we prove the endpoint $L^2_t L^\infty_x$ estimate for $n\ge 3$, and the $L^q_t L^\infty_x$ estimate
         with $2<q<\infty$ for $n=2$.

         This paper deals with the low regularity local well-posed and il1-posed theory in H^s for semilinear wave equations with polynomial
         nonlinearity in u and \partial u. The ill-posed result concerns the focusing type equations with nonlinearity on u and \partial_t u.

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Some Links :

Last modified: Aug 09, 2009.