
Giga, Yoshikazu; Gries, Mathis; Hieber, Matthias; Hussein, Amru; Kashiwabara, Takahito
Consider the 3d primitive equations in a layer domain Ω = G×(−h,0), G = (0,1)2, subject to mixed Dirichlet and Neumann boundary conditions at z = −h and z = 0, respectively, and the periodic lateral boundary condition. It is shown that this equation is globally, strongly wellposed for arbitrary large data of the form a = a1 + a2, where a1 ∈ C(G;Lp(−h,0)), a2 ∈ L∞(G;Lp(−h,0)) for p > 3, and where a1 is periodic in the horizontal variables and a2 is suﬃciently small. In particular, no diﬀerentiability condition on the data is assumed. The approach relies on L∞...

Hamamuki, Nao
In the classical level set method, the slope of solutions can be very small or large, and it can make it diﬃcult to get the precise level set numerically. In this paper, we introduce an improved level set equation whose solutions are close to the signed distance function to evolving interfaces. The improved equation is derived via approximation of the evolution equation for the distance function. Applying the comparison principle, we give an upper and lower bound near the zero level set for the viscosity solution to the initial value problem.

Giga, Yoshikazu
This is essentially a survey paper on a large time behavior of solutions of some simple birth and spread models to describe growth of crystal surfaces. The models discussed here include levelset ﬂow equations of eikonal or eikonalcurvature ﬂow equations with source terms. Large time asymptotic speed called growth rate is studied. As an application, a simple proof is given for asymptotic proﬁle of crystal grown by anisotropic eikonalcurvature ﬂow.

Giga, Yoshikazu; Gries, Mathis; Hieber, Matthias; Hussein, Amru; Kashiwabara, Takahito
This article presents the maximal regularity approach to the primitive equations. It is proved that the 3D primitive equations on cylindrical domains admit a unique, global strong solution for initial data lying in the critical solonoidal Besov space B2/p pq for p,q ∈ (1,∞) with 1/p + 1/q ≤ 1. This solution regularize instantaneously and becomes even real analytic for t > 0.

Fukuda, Ikki
We study the asymptotic behavior of global solutions to the initial value problem for the generalized KdVBurgers equation. One can expect that the solution to this equation converges to a selfsimilar solution to the Burgers equation, due to earlier works related to this problem. Actually, we obtain the optimal asymptotic rate similar to those results and the second asymptotic proﬁle for the generalized KdVBurgers equation.

Giga, Yoshikazu; Gries, Mathis; Hieber, Matthias; Hussein, Amru; Kashiwabara, Takahito
Consider the primitive equations on R2 ×(z0, z1) with initial data a of the form a = a1 +a2, where a1 ∈ BUCσ(R2; L1(z0, z1)) and a2 ∈ L∞σ (R2; L1(z0, z1)) and where BUCσ(L1) and L∞σ (L1) denote the space of all solenoidal, bounded uniformly continuous and all solenoidal, bounded functions on R2, respectively, which take values in L1 (z0, z1). These spaces are scaling invariant and represent the anisotropic character of these equations. It is shown that, if ka2kL∞σ (L1) is sufficiently small, then this set of equations has a unique, local, mild solution. If in addition a...

Ishikawa, Goo
We give stabilization and parametrization theorems for a class of singular varieties in the space of polynomials of one variable and generalize the results of Arnol'd and Givental'. The class contains the open swallowtails and the open Whitney umbrella. The parametrization is associated with the singularity of a stable mapping (in the sense of Thorn and Mather) of kernel rank one.

Ishikawa, Goo
We give stabilization and parametrization theorems for a class of singular varieties in the space of polynomials of one variable and generalize the results of Arnol'd and Givental'. The class contains the open swallowtails and the open Whitney umbrella. The parametrization is associated with the singularity of a stable mapping (in the sense of Thorn and Mather) of kernel rank one.

Ishikawa, Goo
We give stabilization and parametrization theorems for a class of singular varieties in the space of polynomials of one variable and generalize the results of Arnol'd and Givental'. The class contains the open swallowtails and the open Whitney umbrella. The parametrization is associated with the singularity of a stable mapping (in the sense of Thorn and Mather) of kernel rank one.

Ishikawa, Goo
We give stabilization and parametrization theorems for a class of singular varieties in the space of polynomials of one variable and generalize the results of Arnol'd and Givental'. The class contains the open swallowtails and the open Whitney umbrella. The parametrization is associated with the singularity of a stable mapping (in the sense of Thorn and Mather) of kernel rank one.

Ishikawa, Goo
We give stabilization and parametrization theorems for a class of singular varieties in the space of polynomials of one variable and generalize the results of Arnol'd and Givental'. The class contains the open swallowtails and the open Whitney umbrella. The parametrization is associated with the singularity of a stable mapping (in the sense of Thorn and Mather) of kernel rank one.

Okabe, Yasunori

Okabe, Yasunori

Okabe, Yasunori

Okabe, Yasunori

Okabe, Yasunori

Kubota, K.

Kubota, K.

Kubota, K.

Kubota, K.