Mathematical Fluid Mechanics and Related Topics - in honor of Professor Hideo Kozono's sixtieth birthday - 6 Sep 2018

We rewrite the standard Hardy inequality in the form of an equality with radial derivative in for . Then we present another Hardy inequalities with radial and spherical derivatives in for . We al...

This talk is based on my recent jointwork with Kazumasa Fujiwara, Scuola Normale Superiore di Pisa. We give a sharp upper bound of lifespan of blowup solutions to the Cauchy problem for a generalized derivative nonlinear Schrödinger equations with...

Celebrating Approximate 60s -- An International Conference on Nonlinear PDEs and Its Applications at NYU Shanghai 19 Jun 2018

We rewrite the standard Hardy inequality in the form of an equality with radial derivative in for . Then we present another Hardy inequalities with radial and spherical derivatives in for . We al...

Mathematical Theory of turbulence by the method of modern analysis and computational science

Project Year: May 2012 - Mar 2017

The challenging problem on global well-posedness of the Navier-Stokes equations had been so fully investigated that several remarkable results are obtained. Furthermore, our DNS of the uniformly isotropic turbulence is still by far the larger comp...

Blow-up phenomenon of positive solutions to the Cauchy problem for nonlinear heat equation of Fujita type is studied. The blow-up phenomenon was first observed and proved by Hiroshi Fujita about half a century ago. There is a large literature on t...

We studied nonlinear elliptic equations arising in various fields of mathematical physics by means of variational analysis, ordinary differential equations, and viscosity techniques. We studied orbital stability of standing waves, explicit blow-up...

Various types of nonlinear PDEs (nonlinear elliptic equations, nonlinear diffusion equations, nonlinear wave equations, nonlinear Schrodinger equations) arising in physics and engineering were synthetically studied from the viewpoint of the theory...