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In this paper we consider nonnegative solutions of the following parabolic-elliptic cross-diffusion system \begin{equation*} \left\{ \begin{array}{l} \begin{aligned} &u_t = \Delta u - \nabla(u f(|\nabla v|^2 )\nabla v), \\[6pt] &0= \Delta v -\mu + u , \quad \int_{\Omega}v =0, \ \ \mu := \frac 1 {|\Omega|} \int_{\Omega} u dx, \\[6pt] &u(x,0)= u_0(x), \end{aligned} \end{array} \right. \end{equation*} in $\Omega \times (0,\infty)$, with $\Omega$ a ball in $\mathbb{R}^N$, $N\geq 3$ under homogeneous Neumann boundary conditions and $f(\xi) = (1+ \xi)^{-\alpha}$, $0<\alpha < \frac{N-2}{2(N-1)}$, which describes gradient-dependent limitation of cross diffusion fluxes. Under conditions on $f$ and initial data, we prove that a solution which blows up in finite time in $L^\infty$-norm, blows up also in $L^p$-norm for some $p>1$. Moreover, a lower bound of blow-up time is derived. \vskip.2truecm \noindent{\bf AMS Subject Classification }{Primary: 35B44; Secondary: 35Q92, 92C17.} \vskip.2truecm \noindent{\bf Key Words:} finite-time blow-up; chemotaxis., Comment: 18 pages

A solar occultation sensor, the Improved Limb Atmospheric Spectrometer (ILAS)-II, measured 5890 vertical profiles of ozone concentrations in the stratosphere and lower mesosphere and of other species from January to October 2003. The measurement latitude coverage was 54-71degN and 64-88degS, which is similar to the coverage of ILAS (November 1996 to June 1997). One purpose of the ILAS-II measurements was to continue such high-latitude measurements of ozone and its related chemical species in order to help accurately determine their trends. The present paper assesses the quality of ozone data in the version 1.4 retrieval algorithm, through comparisons with results obtained from comprehensive ozonesonde measurements and four satellite-borne solar occultation sensors. In the Northern Hemisphere (NH), the ILAS-II ozone data agree with the other data within +/-10% (in terms of the absolute difference divided by its mean value) at altitudes between 11 and 40 km, with the median coincident ILAS-II profiles being systematically up to 10% higher below 20 km and up to 10% lower between 21 and 40 km after screening possible suspicious retrievals. Above 41 km, the negative bias between the NH ILAS-II ozone data and the other data increases with increasing altitude and reaches 30% at 61-65 km. In the Southern Hemisphere, the ILAS-II ozone data agree with the other data within 10% in the altitude range of 11-60 km, with the median coincident profiles being on average up to 10% higher below 20 km and up to 10% lower above 20 km.

The Improved Limb Atmospheric Spectrometer (ILAS) II on board the Advanced Earth Observing Satellite (ADEOS) II observed stratospheric aerosol in visible/near-infrared/infrared spectra over high latitudes in the Northern and Southern Hemispheres. Observations were taken intermittently from January to March, and continuously from April through October, 2003. We assessed the data quality of ILAS-II version 1.4 aerosol extinction coefficients at 780 nm from comparisons with the Stratospheric Aerosol and Gas Experiment (SAGE) II, SAGE III, and the Polar Ozone and Aerosol Measurement (POAM) III aerosol data. At heights below 20 km in the Northern Hemisphere, aerosol extinction coefficients from ILAS-II agreed with those from SAGE II and SAGE III within 10%, and with those from POAM III within 15%. From 20 to 26 km, ILAS-II aerosol extinction coefficients were smaller than extinction coefficients from the other sensors; differences between ILAS-II and SAGE II ranged from 10% at 20 km to 34% at 26 km. ILAS-II aerosol extinction coefficients from 20 to 25 km in February over the Southern Hemisphere had a negative bias (12-66%) relative to SAGE II aerosol data. The bias increased with increasing altitude. Comparisons between ILAS-II and POAM III aerosol extinction coefficients from January to May in the Southern Hemisphere (defined as the non-Polar Stratospheric Cloud (PSC) season ) yielded qualitatively similar results. From June to October (defined as the PSC season ), aerosol extinction coefficients from ILAS-II were smaller than those from POAM III above 17 km, as in the case of the non-PSC season; however, ILAS-II and POAM III aerosol data were within 15% of each other from 12 to 17 km.