3 citations · 11 across the 21 of their papers we have counts for
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On the uniqueness of the quasi-geostrophic equation with the fractional Laplacian
Tsukasa Iwabuchi, Taiki Okazaki
We consider the uniqueness of the solution of the surface quasi-geostrophic equation with fractional Laplacian. We show that the uniqueness holds in non-homogeneous Besov spaces wi…
Sharp well-posedness and ill-posedness of the stationary quasi-geostrophic equation
Mikihiro Fujii, Tsukasa Iwabuchi
We consider the stationary problem for the quasi-geostrophic equation on the whole plane and investigate its well-posedness and ill-posedness. In[Fujii, Ann. PDE 10, 10 (2024)], it…
The Derivative Structure for a Quadratic Nonlinearity and Uniqueness for SQG
Tsukasa Iwabuchi
We study the two-dimensional surface quasi-geostrophic equation on a bounded domain with a smooth boundary. Motivated by the three-dimensional incompressible Navier-Stokes equation…
On the uniqueness of the mild solution of the critical quasi-geostrophic equation
Tsukasa Iwabuchi, Taiki Okazaki
We demonstrate that the uniqueness of the mild solution of the two-dimensional quasi-geostrophic equation with the critical dissipation holds in the scaling critical homogeneous Be…
Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations
Tsukasa Iwabuchi, Dáithí Ó hAodha
We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay…
Remark on the uniqueness of the mild solution of SQG equation
Tsukasa Iwabuchi, Ryoma Ueda
We study the two-dimensional surface quasi-geostrophic equation. Motivated by the uniqueness for the three-dimensional incompressible Navier-Stokes equations, we demonstrate that t…
Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier-Stokes Equations
Tsukasa Iwabuchi, Dáithí Ó hAodha
We discuss optimal estimates of solutions to the compressible Navier-Stokes equations in Besov norms. In particular, we consider the estimate of the curl-free part of the solution…
On the ill-posedness for the full system of compressible Navier-Stokes equations
Motofumi Aoki, Tsukasa Iwabuchi
We consider the Cauchy problem for compressible Navier--Stokes equations of the ideal gas in the three-dimensional spaces. It is known that the Cauchy problem in the scaling critic…
Energy conservation law for weak solutions of the full compressible Navier-Stokes equations
Motofumi Aoki, Tsukasa Iwabuchi
We consider a sufficient condition for the energy conservation law of a weak solution for the full compressible Navier-Stokes equations on the torus. We prove that a weak solution…
An application of spectral localization to critical SQG on a ball
Tsukasa Iwabuchi
We study the Cauchy problem for the quasi-geostrophic equations in a unit ball of the two dimensional space with the homogeneous Dirichlet boundary condition. We show the existence…
Large-Time Behaviour of Solutions to the Surface Quasi-Geostrophic Equations
Dáithí Ó hAodha, Tsukasa Iwabuchi
We construct a linear approximation of the solution to the Surface Quasi-Geostrophic Equation in , and obtain a convergence rate in between the solution and thi…
On analyticity up to the boundary for critical quasi-geostrophic equations
Tsukasa Iwabuchi
We study the Cauchy problem for the quasi-geostrophic equations with the critical dissipation in the two dimensional half space under the homogeneous Dirichlet boundary condition.…
Analyticity and large time behavior for the Burgers equation with the critical dissipation
Tsukasa Iwabuchi
This paper is concerned with the Cauchy problem of the Burgers equation with the critical dissipation. The well-posedness and analyticity in both of the space and the time variable…
On self-similar solutions to degenerate compressible Navier-Stokes equations
Pierre Germain, Tsukasa Iwabuchi, Tristan Léger
We study cavitating self-similar solutions to compressible Navier-Stokes equations with degenerate density-dependent viscosity. We prove both existence of expanders and non-existen…
Backward self-similar solutions for compressible Navier-Stokes equations
Pierre Germain, Tsukasa Iwabuchi, Tristan Léger
This article is devoted to backward self-similar blow up solutions of the compressible Navier-Stokes equations with radial symmetry. We show that such solutions cannot exist if the…
The Leibniz rule for the Dirichlet and the Neumann Laplacian
Tsukasa Iwabuchi
We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half sp…
Self-similar solutions for compressible Navier-Stokes equations
Pierre Germain, Tsukasa Iwabuchi
We construct forward self-similar solutions (expanders) for the compressible Navier-Stokes equations. Some of these self-similar solutions are smooth, while others exhibit a singul…
The semigroup generated by the Dirichlet Laplacian of fractional order
Tsukasa Iwabuchi
In the whole space , linear estimates for heat semi-group in Besov spaces are well established, which are estimates of - type, maximal regularity, e.t.c. Thi…
Existence of mild solutions for the Hamilton-Jacobi equation with critical fractional viscosity in the Besov spaces
Tsukasa Iwabuchi, Tatsuki Kawakami
We consider the Cauchy problem for the Hamilton-Jacobi equation with critical dissipation, $$ \partial_t u + (-Δ)^{ 1/2} u = |\nabla u|^p, \quad x \in \mathbb R^N, t > 0, \qquad u(…